some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

multiscale aggregating discontinuities a method for circumventing loss of material stability new methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described these methods called multiscale aggregating discontinuities are based on the concept of perforated unit cells which exclude subdomains that are unstable i e exhibit loss of material stability using this concept it is possible to compute an equivalent discontinuity at the coarser scale including both the direction of the discontinuity and the magnitude of the jump these variables are then passed to the coarse scale model along with the stress in the unit cell the discontinuity is injected at the coarser scale by the extended finite element method analysis of the procedure shows that the method is consistent in power and yields a bulk stress strain response that is stable applications of this procedure to crack growth in heterogeneous materials are given copyright 2007 john wiley sons ltd

a multiscale projection method for macro microcrack simulations we present a new multiscale method for crack simulations this approach is based on a two scale decomposition of the displacements and a projection to the coarse scale by using coarse scale test functions the extended finite element method xfem is used to take into account macrocracks as well as microcracks accurately the transition of the field variables between the different scales and the role of the microfield in the coarse scale formulation are emphasized the method is designed so that the fine scale computation can be done independently of the coarse scale computation which is very efficient and ideal for parallelization several examples involving microcracks and macrocracks are given it is shown that the effect of crack shielding and amplification for crack growth analyses can be captured efficiently copyright 2007 john wiley sons ltd

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

modeling repeated functional observations we introduce a new methodological framework for repeatedly observed and thus dependent functional data aiming at situations where curves are recorded repeatedly for each subject in a sample our methodology covers the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies where the timing of recordings is often sparse and random the proposed models lead to an interpretable and straightforward decomposition of the inherent variation in repeatedly observed functional data and are implemented through a straightforward two step functional principal component analysis we provide consistency results and asymptotic convergence rates for the estimated model components we compare the proposed model with an alternative approach via a two dimensional karhunen loeve expansion and illustrate it through the analysis of longitudinal mortality data from period lifetables that are repeatedly observed for a sample of countries over ma

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

low rank scale invariant tensor product smooths for generalized additive mixed models summary a general method for constructing low rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented a penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately these marginal smooths being represented using a low rank basis with an associated quadratic wiggliness penalty the smooths offer several advantages i they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates making them useful when there is no natural way to scale covariates relative to each other ii they have a useful tuneable range of smoothness unlike single penalty tensor product smooths that are scale invariant iii the relatively low rank of the smooths means that they are computationally efficient iv the penalties on the smooths are easily interpretable in terms of function shape v the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task and vi the smooths can easily be written as components of a standard linear or generalized linear mixed model allowing them to be used as components of the rich family of such models implemented in standard software and to take advantage of the efficient and stable computational methods that have been developed for such models a small simulation study shows that the methods can compare favorably with recently developed smoothing spline anova methods

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

stable and efficient multiple smoothing parameter estimation for generalized additive models representation of generalized additive models gam s using penalized regression splines allows gam s to be employed in a straightforward manner using penalized regression methods not only is inference facilitated by this approach but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross validation the current fitting and smoothing parameter selection methods for such models are usually effective but do not provide the level of numerical stability to which users of linear regression packages for example are accustomed in particular the existing methods cannot deal adequately with numerical rank deficiency of the gam fitting problem and it is not straightforward to produce methods that can do so given that the degree of rank deficiency can be smoothing parameter dependent in addition models with the potential flexibility of gam s can also present

a regularized phenomenological multiscale damage model summary we present a regularized phenomenological multiscale model where elastic properties are computed using direct homogenization and subsequently evolved using a simple three parameter orthotropic continuum damage model the salient feature of the model is a unified regularization framework based on the concept of effective softening strain the unified regularization scheme has been employed in the context of constitutive law rescaling and the staggered nonlocal approach we show that an element erosion technique for crack propagation when exercised with one of the two regularization schemes 1 possesses a characteristic length 2 is consistent with fracture mechanics approach and 3 does not suffer from pathological mesh sensitivity copyright 2014 john wiley sons ltd

smoothing spline gaussian regression more scalable computation via efficient approximation summary smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with gaussian responses the computation of smoothing splines is generally of the order o n3 n being the sample size which severely limits its practical applicability we study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient a simple algorithm is presented and the bayes model that is associated with the approximations is derived with the latter guiding the porting of bayesian confidence intervals the practical choice of the dimension of the approximating space is determined through simulation studies and empirical comparisons of the approximations with the exact solution are presented also evaluated is a simple modification of the generalized cross validation method for smoothing parameter selection which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross validation

generalized additive models for exceedances of high thresholds with an application to return level estimation for u s wind gusts generalized additive model gam forms offer a flexible approach to capturing marginal variation such forms are used here to represent distributional variation in extreme values and presented in t

parameterization of multivariate random effects models for categorical data alternative parameterizations and problems of identification and estimation of multivariate random effects models for categorical responses are investigated the issues are illustrated in the context of the multivariate binomial logit normal bln model introduced by coull and agresti 2000 biometrics 56 73 80 we demonstrate that the bln model is poorly identified unless proper restrictions are imposed on the parameters moreover estimation of bln models is unduly computationally complex in the first application considered by coull and agresti an identification problem results in highly unstable highly correlated parameter estimates and large standard errors a probit normal version of the specified bln model is demonstrated to be underidentified whereas the bln model is empirically underidentified identification can be achieved by constraining one of the parameters we show that a one factor probit model is equivalent to the probit version of the specified bln model and that a one factor logit model is empirically equivalent to the bln model estimation is greatly simplified by using a factor model

multiscale adaptive regression models for neuroimaging data neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations called voxels on a two dimensional 2d surface or in a 3d volume conventional analyses of imaging data include two sequential steps spatially smoothing imaging data and then independently fitting a statistical model at each voxel however conventional analyses suffer from the same amount of smoothing throughout the whole image the arbitrary choice of smoothing extent and low statistical power in detecting spatial patterns we propose a multiscale adaptive regression model marm to integrate the propagation separation ps approach polzehl and spokoiny 2000 2006 with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects marm has three features being spatial being hierarchical and being adaptive we use a multiscale adaptive estimation and testing procedure maet to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics theoretically we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics our simulation studies and real data analysis confirm that marm significantly outperforms conventional analyses of imaging data

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

hierarchical modeling of heterogeneous solids in this paper a methodology is introduced for the development of adaptive methods for hierarchical modeling of elastic heterogeneous bodies the approach is based on the idea of computing an estimate of the modeling error introduced by replacing the actual fine scale material tensor with that of a homogenized material and to adaptively refine the material description until a prespecified error tolerance is met this process generates a family of coarse scale solutions in which the solution corresponding to the fine scale model of the body which embodies the exact microstructure loading and boundary conditions represents the highest level of sophistication in a family of continuum models the adaptive strategy developed can lead to a new non uniform description of material properties which reflects the loading and boundary conditions a post processing technique is also introduced which endows the coarse scale solutions with fine scale information through a local solution process convergence of the adaptive algorithm is proven and modeling error estimates as a function of scale of material description are presented preliminary results of several numerical experiments are given to confirm estimates and to illustrate the promise of the approach in practical applications

linear mixed effects modeling approach to fmri group analysis conventional group analysis is usually performed with student type t test regression or standard an c ova in which the variance covariance matrix is presumed to have a simple structure some correction approaches are adopted when assumptions about the covariance structure is violated however as experiments are designed with different degrees of sophistication these traditional methods can become cumbersome or even be unable to handle the situation at hand for example most current fmri software packages have difficulty analyzing the following scenarios at group level 1 taking within subject variability into account when there are effect estimates from multiple runs or sessions 2 continuous explanatory variables covariates modeling in the presence of a within subject repeated measures factor multiple subject grouping between subjects factors or the mixture of both 3 subject specific adjustments in covariate modeling 4 group analysis with estimation of hemodynamic response hdr function by multiple basis functions 5 various cases of missing data in longitudinal studies and 6 group studies involving family members or twins here we present a linear mixed effects modeling lme methodology that extends the conventional group analysis approach to analyze many complicated cases including the six prototypes delineated above whose analyses would be otherwise either difficult or unfeasible under traditional frameworks such as an c ova and general linear model glm in addition the strength of the lme framework lies in its flexibility to model and estimate the variance covariance structures for both random effects and residuals the intraclass correlation icc values can be easily obtained with an lme model with crossed random effects even at the presence of confounding fixed effects the simulations of one prototypical scenario indicate that the lme modeling keeps a balance between the control for false positives and the sensitivity for activation detection the importance of hypothesis formulation is also illustrated in the simulations comparisons with alternative group analysis approaches and the limitations of lme are discussed in details

multiple scale eigendeformation based reduced order homogenization multiple scale eigendeformation based reduced order homogenization method which provides considerable computational cost saving in comparison to the direct homogenization method has been developed verified against the direct homogenization method and validated against experimental data the salient feature of the method is in the formulation of the unit cell problem in terms of residual free stresses and therefore eliminating the need for costly equilibrium calculations required by the direct homogenization method this is accomplished by introducing discretized eigendeformation fields at different scales which are collectively referred to as eigenstrains and eigenseparations and then precomputing a sequence of elasticity solutions of the unit cell problem subjected to the eigendeformation fields prior to nonlinear analysis

wavelet based functional mixed models increasingly scientific studies yield functional data in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid we present new methodology that generalizes the linear mixed model to the functional mixed model framework with model fitting done by using a bayesian wavelet based approach this method is flexible allowing functions of arbitrary form and the full range of fixed effects structures and between curve covariance structures that are available in the mixed model framework it yields nonparametric estimates of the fixed and random effects functions as well as the various between curve and within curve covariance matrices the functional fixed effects are adaptively regularized as a result of the non linear shrinkage prior that is imposed on the fixed effects wavelet coefficients and the random effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient because we have posterior samples for all model quantities we can perform pointwise or joint bayesian inference or prediction on the quantities of the model the adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks

group analysis of dti fiber tract statistics with application to neurodevelopment abstract diffusion tensor imaging dti provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures this paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images the diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics diffusion properties such as fractional anisotropy fa and tensor norm along fiber tracts are modeled as multivariate functions of arc length hypothesis testing is performed non parametrically using permutation testing based on the hotelling t 2 statistic the linear discriminant embedded in the t 2 metric provides an intuitive localized interpretation of detected differences the proposed methodology was tested on two clinical studies of neurodevelopment in a study of 1 and 2 year old subjects a significant increase in fa and a correlated decrease in frobenius norm was found in several tracts significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly mvm demonstrating the potential of this method for clinical studies

hybrid impotent incompatible eigenstrain based homogenization summary we present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables the method is based on a variant of the transformation field analysis tfa where eigenstrains are discretized using c 0 continuous approximation in matrix dominated mode of deformation hereafter referred to as impotent eigenstrain mode whereas in multiphase mode of deformation the eigenstrains are approximated using the usual c 1 approximation the delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase both characteristic to averaging methods are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases the proposed formulation has been verified against a direct numerical simulation the method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium copyright 2013 john wiley sons ltd

a staggered nonlocal multiscale model for a heterogeneous medium summary a staggered nonlocal multiscale model for a heterogeneous medium is developed and validated the model is termed as staggered nonlocal in the sense that it employs current information for the point under consideration and past information from its local neighborhood for heterogeneous materials the concept of phase nonlocality is introduced by which nonlocal phase eigenstrains are computed using different nonlocal phase kernels the staggered nonlocal multiscale model has been found to be insensitive to finite element mesh size and load increment size furthermore the computational overhead in dealing with nonlocal information is mitigated by superior convergence of the newton method copyright 2012 john wiley sons ltd

mixed effects smoothing spline analysis of variance we propose a general family of nonparametric mixed effects models smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function the random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters these parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method we derive a connection between a nonparametric mixed effects model and a linear mixed effects model this connection suggests a way of fitting a nonparametric mixed effects model by using existing programs the classical two way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis of variance decompositions to build nonparametric mixed effects models similarly to the classical analysis of variance components of these nonparametric mixed effects models can be interpreted as main effects and interactions the penalized likelihood estimates of the fixed effects in a two way mixed model are extensions of james stein shrinkage estimates to correlated observations in an example three nested nonparametric mixed effects models are fitted to a longitudinal data set

identifying the finite dimensionality of curve time series the curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup we propose a new method to identify the dimensionality of curve time series based on the dynamical dependence across different curves the practical implementation of our method boils down to an eigenanalysis of a finite dimensional matrix furthermore the determination of the dimensionality is equivalent to the identification of the nonzero eigenvalues of the matrix which we carry out in terms of some bootstrap tests asymptotic properties of the proposed method are investigated in particular our estimators for zero eigenvalues enjoy the fast convergence rate n while the estimators for nonzero eigenvalues converge at the standard n rate the proposed methodology is illustrated with both simulated and real data sets

smoothing spline models with correlated random errors abstract spline smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model their performances depend greatly on the choice of smoothing parameters many methods of selecting smoothing parameters such as generalized maximum likelihood gml generalized cross validation gcv and unbiased risk ubr have been developed under the assumption of independent observations they tend to underestimate smoothing parameters when data are correlated in this article i assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters i extend the gml gcv and ubr methods to estimate the smoothing parameters and the correlation parameters simultaneously i also relate a smoothing spline model to three mixed effects models these relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction blup estimates and that the gml estimates of the smoothing parameters an

tensor graphical lasso teralasso the paper introduces a multiway tensor generalization of the bigraphical lasso which uses a two way sparse kronecker sum multivariate normal model for the precision matrix to model parsimoniously conditional dependence relationships of matrix variate data based on the cartesian product of graphs we call this tensor graphical lasso generalization teralasso we demonstrate by using theory and examples that the teralasso model can be accurately and scalably estimated from very limited data samples of high dimensional variables with multiway co ordinates such as space time and replicates statistical consistency and statistical rates of convergence are established for both the bigraphical lasso and teralasso estimators of the precision matrix and estimators of its support non sparsity set respectively we propose a scalable composite gradient descent algorithm and analyse the computational convergence rate showing that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to the global minimizer of the teralasso objective function finally we illustrate teralasso by using both simulation and experimental data from a meteorological data set showing that we can accurately estimate precision matrices and recover meaningful conditional dependence graphs from high dimensional complex data sets

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

properties of principal component methods for functional and longitudinal data analysis the use of principal component methods to analyze functional data is appropriate in a wide range of different settings in studies of functional data analysis it has often been assumed that a sample of random functions is observed precisely in the continuum and without noise while this has been the traditional setting for functional data analysis in the context of longitudinal data analysis a random function typically represents a patient or subject who is observed at only a small number of randomly distributed points with nonnegligible measurement error nevertheless essentially the same methods can be used in both these cases as well as in the vast number of settings that lie between them how is performance affected by the sampling plan in this paper we answer that question we show that if there is a sample of n functions or subjects then estimation of eigenvalues is a semiparametric problem with root n consistent estimators even if only a few observations are made of each function and if each observation is encumbered by noise however estimation of eigenfunctions becomes a nonparametric problem when observations are sparse the optimal convergence rates in this case are those which pertain to more familiar function estimation settings we also describe the effects of sampling at regularly spaced points as opposed to random points in particular it is shown that there are often advantages in sampling randomly however even in the case of noisy data there is a threshold sampling rate depending on the number of functions treated above which the rate of sampling either randomly or regularly has negligible impact on estimator performance no matter whether eigenfunctions or eigenvectors are being estimated

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

functional linear regression analysis for longitudinal data we propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data where both the predictor and response are functions of a covariate such as time predictor and response processes have smooth random trajectories and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects in longitudinal studies the number of repeated measurements per subject is often small and may be modeled as a discrete random number and accordingly only a finite and asymptotically nonincreasing number of measurements are available for each subject or experimental unit we propose a functional regression approach for this situation using functional principal component analysis where we estimate the functional principal component scores through conditional expectations this allows the prediction of an unobserved response trajectory from sparse measurements of a predictor trajectory the resulting technique is flexible and allows for different patterns regarding the timing of the measurements obtained for predictor and response trajectories asymptotic properties for a sample of n subjects are investigated under mild conditions as n oo and we obtain consistent estimation for the regression function besides convergence results for the components of functional linear regression such as the regression parameter function we construct asymptotic pointwise confidence bands for the predicted trajectories a functional coefficient of determination as a measure of the variance explained by the functional regression model is introduced extending the standard r 2 to the functional case the proposed methods are illustrated with a simulation study longitudinal primary biliary liver cirrhosis data and an analysis of the longitudinal relationship between blood pressure and body mass index

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

spline smoothing and optimal rates of convergence in nonparametric regression models linear estimation is considered in nonparametric regression models of the form yi f xi ei xi e a b where the zero mean errors are uncorrelated with common variance a2 and the response function f is assumed only to have a bounded square integrable qth derivative the linear estimator which minimizes the maximum mean squared error summed over the observation points is derived and the exact minimax rate of convergence is obtained for practical problems where bounds on 11 f2q 11 and a2 may be unknown generalized cross validation is shown to give an adaptive estimator which achieves the minimax optimal rate under the additional assumption of normality 1 the model consider the nonparametric regression model

fadtts functional analysis of diffusion tensor tract statistics the aim of this paper is to present a functional analysis of a diffusion tensor tract statistics fadtts pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest such as age diagnostic status and gender and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies the fadtts integrates five statistical tools i a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates ii a weighted least squares estimation of the varying coefficient functions iii a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties iv a global test statistic to test hypotheses of interest and v a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions simulated data are used to evaluate the finite sample performance of fadtts we apply fadtts to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment fadtts can be used to facilitate the understanding of normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles the advantages of fadtts compared with the other existing approaches are that they are capable of modeling the structured inter subject variability testing the joint effects and constructing their simultaneous confidence bands however fadtts is not crucial for estimation and reduces to the functional analysis method for the single measure

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

multiscale structural topology optimization with an approximate constitutive model for local material microstructure abstract this paper builds on our recent work xia and breitkopf 2014 on multiscale structural topology optimization where at the microscopic scale local materials are optimized concurrently according to current loading status the former design framework requires intensive computational cost due to large number of repetitive local material optimizations to circumvent this limitation in the present work we construct a reduced database model viewing the local material optimization process as a generalized constitutive behavior using separated representations in this model the database is built from a set of numerical experiments of local material optimizations in the macroscopic strain tensor space each value in the database corresponds to the strain energy density evaluated on a material microstructure optimized according to the imposed macroscopic strain by tensor decomposition a continuous representation of the strain energy density is built as a sum of products of one dimensional interpolation functions as a result of this a priori off line step the effective strain energy and stress strain relations required for macroscopic structural evaluation and optimization are provided in a numerically explicit manner the results given by the reduced database model are compared with full scale results it is also shown that this explicit constitutive behavior representation can well serve multiscale structural design at a significantly reduced computational cost

statistical inference in mixed models and analysis of twin and family data analysis of data from twin and family studies provides the foundation for studies of disease inheritance the development of advanced theory and computational software for general linear models has generated considerable interest for using mixed effect models to analyze twin and family data as a computationally more convenient and theoretically more sound alternative to the classical structure equation modeling despite the long history of twin and family data analysis some fundamental questions remain unanswered we addressed two important issues one is to determine the necessary and sufficient conditions for the identifiability in the mixed effects models for twin and family data the other is to derive the asymptotic distribution of the likelihood ratio test which is novel due to the fact that the standard regularity conditions are not satisfied we considered a series of specific yet important examples in which we demonstrated how to formulate mixed effect models to appropriately reflect the data and our key idea is the use of the cholesky decomposition finally we applied our method and theory to provide a more precise estimate of the heritability of two data sets than the previously reported estimate

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

a robust and unified framework for estimating heritability in twin studies using generalized estimating equations the heritability of a phenotype measures the proportion of trait variance due to genetic factors in a population in the past 50 years studies with monozygotic and dizygotic twins have estimated heritability for 17 804 traits 1 thus twin studies are popular for estimating heritability researchers are often interested in estimating heritability for non normally distributed outcomes such as binary counts skewed or heavy tailed continuous traits in these settings the traditional normal ace model nace and falconer s method can produce poor coverage of the true heritability therefore we propose a robust generalized estimating equations gee2 framework for estimating the heritability of non normally distributed outcomes the traditional nace and falconer s method are derived within this unified gee2 framework which additionally provides robust standard errors although the traditional falconer s method cannot adjust for covariates the corresponding gee2 falconer can incorporate mean and variance level covariate effects e g let heritability vary by sex or age given a non normally distributed outcome the gee2 models are shown to attain better coverage of the true heritability compared to traditional methods finally a scenario is demonstrated where nace produces biased estimates of heritability while falconer remains unbiased therefore we recommend gee2 falconer for estimating the heritability of non normally distributed outcomes in twin studies

a multi scale spectral stochastic method for homogenization of multi phase periodic composites with random material properties in this work a spectral stochastic computational scheme is proposed that links the global properties of multi phase periodic composites to the geometry and random material properties of their microstructural components to propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on hermite chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought a full stochastic description of the global effective properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell a representative subset of results is compared with the results obtained using monte carlo simulation to demonstrate the accuracy of the proposed procedure copyright 2010 john wiley sons ltd

flexible estimation of covariance function by penalized spline with application to longitudinal family data longitudinal data are routinely collected in biomedical research studies a natural model describing longitudinal data decomposes an individual s outcome as the sum of a population mean function and random subject specific deviations when parametric assumptions are too restrictive methods modeling the population mean function and the random subject specific functions nonparametrically are in demand in some applications it is desirable to estimate a covariance function of random subject specific deviations in this work flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models where the functional forms of the population mean and the subject specific curves are unspecified we estimate nonparametric components of the model by penalized spline p spline biometrics 2001 57 253 259 and reparameterize the random curve covariance function by a modified cholesky decomposition biometrics 2002 58 121 128 which allows for unconstrained estimation of a positive semidefinite matrix to provide smooth estimates we penalize roughness of fitted curves and derive closed form solutions in the maximization step of an em algorithm in addition we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject level source and observation level source we apply these methods to the multi level framingham heart study data to estimate age specific heritability of systolic blood pressure nonparametrically copyright 2011 john wiley sons ltd

optimal smoothing in nonparametric mixed effect models mixed effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures in this article we study an approach to the nonparametric estimation of mixed effect models we consider models with parametric random effects and flexible fixed effects and employ the penalized least squares method to estimate the models the issue to be addressed is the selection of smoothing parameters through the generalized cross validation method which is shown to yield optimal smoothing for both real and latent random effects simulation studies are conducted to investigate the empirical performance of generalized cross validation in the context real data examples are presented to demonstrate the applications of the methodology

pointwise influence matrices for functional response regression we extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors for responses depending linearly on a set of predictors our definition is shown to reduce to the conventional influence matrix for linear models the pointwise degrees of freedom the trace of the pointwise influence matrix are shown to have an adaptivity property that motivates a two step bivariate smoother for modeling nonlinear dependence on a single predictor this procedure adapts to varying complexity of the nonlinear model at different locations along the function and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain

the boundary of negatively curved groups gromov s article gr contains fundamental properties of negatively curved groups several sets of seminar notes are available frn swn usn that contain more detailed accounts of and further expand on gromov s article a sequence xi e r i 1 2 is convergent at infinity provided xi x t 00 as i j t 00 two sequences xi yj convergent at infinityare equivalent if xi yi t 00 as i t 00 a point in the boundary ar of r is an equivalence class of sequences convergent at infinity now r u ar has a natural topology in which r is a discrete subspace and a typical not necessarily open neighborhood of a point a e ar represented by a sequence xj is given by y e r u arj a y n where a y lim xi y if y e r and a y lim xi yi if year is represented by a sequence yj ar is a compact metrizable finite dimensional space gr swn the important tool that relates ar with the cohomological properties of r is the rips complex pd r for every d 0 pd r is the simplicial complex whose vertices are elements of r and a collection xi xk e r spans a simplex if d xi x d for all i j the natural group action of r on itself by left translations gives rise to an action on pd r the key observation of rips is that when d is sufficiently large pd r is contractible and therefore when r is torsion free provides a model for er more precisely we have proposition 1 1 gr lemma 1 7 a swn 4 2 proposition 9 suppose that r is a negatively curved group and let t5 be as in the definition choose an integer

topology of homology manifolds anr homology n manifolds are nite dimensional absolute neighborhood retracts x with the property that for every x 2 x hi x x fxg is 0 for i 6 n and z for i n topological manifolds are natural examples of such spaces to obtain nonmanifold examples we can take a manifold whose boundary consists of a union of integral homology spheres and glue on the cone on each one of the boundary components the resulting space is not a manifold if the fundamental group of any boundary component is a nontrivial perfect group it is a consequence of the double suspension theorem of cannon and edwards that as in the examples above the singularities of polyhedral anr homology manifolds are isolated there are however many examples of anr homology manifolds which have no manifold points whatever see 12 for a good exposition of the relevant theory the purpose of this paper is to begin a surgical classi cation of anr homology manifolds sometimes referred to in the sequel simply as homology manifolds one way to approach this circle of ideas is via the problem of characterizing topological manifolds among anr homology manifolds in cannon s work on the double suspension problem 6 it became clear that in dimensions greater than 4 the right transversality hypothesis is the following weak form of general position

multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method abstract this paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with voronoi cell vcfem for microstructural modeling the voronoi cell finite element model originates from dirichlet tessellation of a representative material element or a base cell in the microstructure homogenized material coefficients for a global displacement finite element model are generated by vcfem analysis using periodic boundary conditions on the base cell following the macroscopic analysis the local vcfem analysis is implemented to depict the true evolution of microstructural stresses and strains various numerical examples are executed for validating the effectiveness of vcfem macro micro modeling of elastic materials the effect of size shape orientation and distribution of heterogeneities on the local and global response are examined

reduced order computational continua abstract we present a new multiscale approach hereafter referred to as reduced order computational continua rc 2 that possesses computational efficiency of phenomenological models for heterogeneous media with accuracy inherent to generalized and nonlocal continua models the rc 2 approach introduces no scale separation makes no assumption about infinitesimality of the fine scale structure does not require higher order continuity introduces no new degrees of freedom is free of higher order boundary conditions and exploits a pre computed material database to effectively solve a unit cell representative volume problem it features three building blocks i the nonlocal quadrature scheme ii the coarse scale stress function and iii the residual free fields the nonlocal quadrature scheme permits nonlocal interactions to extend over finite neighborhoods and thus introduces nonlocality into the two scale integrals employed in the multiple scale asymptotic expansion methods or alternatively into the hill mandel macrohomogeneity condition the coarse scale stress function which replaces the classical notion of coarse scale stress being the average of fine scale stresses is constructed to express the governing equations in terms of coarse scale fields only finally the residual free fields are constructed to avoid costly discrete equilibrium solution of the unit cell problems which is known to be the bottleneck of multiscale computations

nonparametric trend estimation in functional time series with application to annual mortality rates this research was supported by the king abdullah university of science and technology kaust

micro inertia effects in nonlinear heterogeneous media summary the manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large we develop a general purpose computational framework which is valid for nonlinear problems and requires standard c 0 continuous formalism the fine scale inertia effect is accounted for by formulating a quasidynamic unit cell problem where the fine scale inertia effect is represented by so called inertia induced eigenstrain the solution of the nonlinear quasi dynamic unit cell problem gives rise to the modification of either coarse scale mass matrix in the implicit solvers or internal force in the explicit solvers similarly to the classical homogenization theory scale separation is assumed but higher order homogenization is not pursued to avoid higher order coarse scale gradients higher order continuity and higher order boundary conditions numerical examples for both the one dimensional model problem and three dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed copyright 2012 john wiley sons ltd

smoothing parameter and model selection for general smooth models abstractthis article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates gaussian random effects and parametric terms may also be present by construction the method is numerically stable and convergent and enables smoothing parameter uncertainty to be quantified the latter enables us to fix a well known problem with aic for such models thereby improving the range of model selection tools available the smooth functions are represented by reduced rank spline like smoothers with associated quadratic penalties measuring function smoothness model estimation is by penalized likelihood maximization where the smoothing parameters controlling the extent of penalization are estimated by laplace approximate marginal likelihood the methods cover for example generalized additive models for nonexponential family responses e g beta ordered categorical scaled t distribution negative binomial a

modelling and smoothing parameter estimation with multiple quadratic penalties summary penalized likelihood methods provide a range of practical modelling tools including spline smoothing generalized additive models and variants of ridge regression selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from however many modelling problems suggest a formulation employing multiple penalties and here general methodology is lacking a wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimise kw 1 2 xp a y k 2 o p m i 1 iip 0 s i p p is a parameter vector x a design matrix si a non negative definite coefficient matrix defining the i th penalty with associated smoothing parameter ii w a diagonal weight matrix y a vector of data or pseudodata and o an overall smoothing parameter included for reasons of computational efficiency this paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross validation to this problem and how this allows non linear generalized linear and linear models to be fitted using multiple penalties substantially increasing the scope of penalized modelling methods examples of non linear modelling generalized additive modelling and anisotropic smoothing are given

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

finite deformation plasticity for composite structures computational models and adaptive strategies abstract we develop computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures a nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the portion of the macro domain where modeling errors are small whereas elsewhere a more detailed mathematical model based on a piecewise constant approximation of eigenstrains and elastic concentration factors is utilized the methodology is developed within the framework of statistically homogeneous composite material and local periodicity assumptions

covariate adjusted region referenced generalized functional linear model for eeg data electroencephalography eeg studies produce region referenced functional data in the form of eeg signals recorded across electrodes on the scalp it is of clinical interest to relate the highly structured eeg data to scalar outcomes such as diagnostic status in our motivating study resting state eeg is collected on both typically developing td children and children with autism spectrum disorder asd aged 2 to 12 years old the peak alpha frequency paf defined as the location of a prominent peak in the alpha frequency band of the spectral density is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age to retain the most amount of information from the data we consider the oscillations in the spectral density within the alpha band rather than just the peak location as a functional predictor of diagnostic status td vs asd adjusted for chronological age a covariate adjusted region referenced generalized functional linear model is proposed for modeling scalar outcomes from region referenced functional predictors which utilizes a tensor basis formed from one dimensional discrete and continuous bases to estimate functional effects across a discrete regional domain while simultaneously adjusting for additional nonfunctional covariates such as age the proposed methodology provides novel insights into differences in neural development of td and asd children the efficacy of the proposed methodology is investigated through extensive simulation studies

multivariate varying coefficient model for functional responses motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

varying coefficient models and basis function approximations for the analysis of repeated measurements summary a global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying coefficient model with repeated measurements inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly finite sample properties of our procedures are investigated through a simulation study application of the proposed approach is demonstrated through an example in epidemiology in contrast to the existing methods this approach applies whether or not the covariates are timeinvariant and does not require binning of the data when observations are sparse at distinct observation times

adaptive weights smoothing with applications to image restoration we propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data points some theoretical properties of the procedure are investigated then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods finally we discuss applications of this procedure to magnetic resonance and satellite imaging

sur une question d erdos et schinzel ii let f n denote a polynomial with integer coefficients and define h f x y z to be the number of integers not exceeding x for which f n has at least one divisor d such that y

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

statistical inferences for functional data with modem technology development functional data are being observed frequently in many scientific fields a popular method for analyzing such functional data is smoothing first then estimation that is statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another however little is known about this substitution effect on functional data analysis in this paper this problem is investigated when the local polynomial kernel lpk smoothing technique is used for individual function reconstructions we find that under some mild conditions the substitution effect can be ignored asymptotically based on this we construct lpk reconstruction based estimators for the mean covariance and noise variance functions of a functional data set and derive their asymptotics we also propose a gcv rule for selecting good bandwidths for the lpk reconstructions when the mean function also depends on some time independent covariates we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time the lpk reconstruction based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived moreover we propose a l 2 norm based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression the effect of the bandwidths selected by the proposed gcv rule on the accuracy of the lpk reconstructions and the mean function estimator is investigated via a simulation study the proposed methodologies are illustrated via an application to a real functional data set collected in climatology

thin plate regression splines discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data which can be fitted by regression or penalized regression methods the smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother by making use of lanczos iteration the basis change and truncation are computationally efficient the smoothers allow the use of approximate thin plate spline models with large data sets avoid the problems that are associated with knot placement that usually complicate modelling with regression splines or penalized regression splines provide a sensible way of modelling interaction terms in generalized additive models provide low rank approximations to generalized smoothing spline models appropriate for use with large data sets provide a means for incorporating smooth functions of more than one variable into non linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines given that the approach produces spline like models with a sparse basis it also provides a natural way of incorporating unpenalized spline like terms in linear and generalized linear models and these can be treated just like any other model terms from the point of view of model selection inference and diagnostics

fsem functional structural equation models for twin functional data the aim of this article is to develop a novel class of functional structural equation models fsems for dissecting functional genetic and environmental effects on twin functional data while chara

inference in generalized additive mixed modelsby using smoothing splines generalized additive mixed models are proposed for overdispersed and correlated data which arise frequently in studies involving clustered hierarchical and spatial designs this class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression while accounting for correlation between observations by using random effects we estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi likelihood because numerical integration is often required by maximizing the objective functions double penalized quasi likelihood is proposed to make approximate inference frequentist and bayesian inferences are compared a key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software a bias correction procedure is also proposed to improve the performance of double penalized quasi likelihood for sparse data we illustrate the method with an application to infectious disease data and we evaluate its performance through simulation

a simple test for random effects in regression models summary testing that random effects are zero is difficult because the null hypothesis restricts the corresponding variance parameter to the edge of the feasible parameter space in the context of generalized linear mixed models this paper exploits the link between random effects and penalized regression to develop a simple test for a zero effect the idea is to treat the variance components not being tested as fixed at their estimates and then to express the likelihood ratio as a readily computed quadratic form in the predicted values of the random effects under the null hypothesis this has the distribution of a weighted sum of squares of independent standardnormalrandomvariables thetestcanbeusedwithgeneralizedlinearmixedmodels including those estimated by penalized quasilikelihood

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

semiparametric stochastic mixed models for longitudinal data abstract we consider inference for a semiparametric stochastic mixed model for longitudinal data this model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within subject correlation using random effects and a stationary or nonstationary stochastic process we derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function the resulting estimator of the nonparametric function is a smoothing spline we propose and compare frequentist inference and bayesian inference on these model components we use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously we show that estimation of all model components of interest can proceed by fitting a modified linear mixed model we illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations

hypothesis testing in mixture regression models summary we establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models moreover under specific and reasonable conditions we show that the optimal convergence rate of n 1 4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators we also derive the asymptotic distributions of two log likelihood ratio test statistics for testing homogeneity and we propose a resampling procedure for approximating the p value simulation studies are conducted to investigate the empirical performance of the two test statistics finally two real data sets are analysed to illustrate the application of our theoretical results

bridging multiple structural scales with a generalized finite element method summary this paper presents a generalized fem based on the solution of interdependent coarse scale global and fine scale local problems in order to resolve multiscale effects due to fine scale heterogeneities overall structural behavior is captured by the global problem while local problems focus on the resolution of fine scale solution features in regions where material heterogeneities may govern the structural response fine scale problems are accurately solved in parallel and to address the intrinsic coupling of scales these solutions are embedded into the global solution space using a partition of unity approach this method is demonstrated on representative heat transfer examples in order to examine its accuracy efficiency and flexibility copyright 2014 john wiley sons ltd