semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

a robust hybrid method for nonrigid image registration a nonrigid registration method is proposed to automatically align two images by registering two sets of sparse features extracted from the images motivated by the paradigm of robust point matching rpm algorithms 1 2 which were originally proposed for shape registration we develop robust hybrid image matching rhim algorithm by alternatively optimizing feature correspondence and spatial transformation for image registration our rhim algorithm is built to be robust to feature extraction errors a novel dynamic outlier rejection approach is described for removing outliers and a local refinement technique is applied to correct non exactly matched correspondences arising from image noise and deformations experimental results demonstrate the robustness and accuracy of our method

smoothing spline nonlinear nonparametric regression models almost all of the current nonparametric regression methods such as smoothing splines generalized additive models and varyingcoefficients models assume a linear relationship when nonparametric functions are regarded as parameters in this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly they arise in many fields as either theoretical or empirical models our new estimation methods are based on an extension of the gauss newton method to infinite dimensional spaces and the backfitting procedure we extend the generalized cross validation and generalized maximum likelihood methods to estimate smoothing parameters we establish connections between some nonlinear nonparametric models and nonlinear mixed effects models we derive approximate bayesian confidence intervals for inference we illustrate the methods with an application to term structure of interest rates and conduct simulations to evaluate the finite sampl

varying coefficient model with unknown within subject covariance for analysis of tumor growth curves in this article we develop a nonparametric estimation procedure for the varying coefficient model when the within subject covariance is unknown extending the idea of iterative reweighted least squares to the functional setting we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood the covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a kullback leibler criterion empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors

quadratic inference functions for varying coefficient models with longitudinal data nonparametric smoothing methods are used to model longitudinal data but the challenge remains to incorporate correlation into nonparametric estimation procedures in this article we propose an efficient estimation procedure for varying coefficient models for longitudinal data the proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models the proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified for varying coefficient models it is often of interest to test whether coefficient functions are time varying or time invariant we propose a unified and efficient nonparametric hypothesis testing procedure and further demonstrate that the resulting test statistics have an asymptotic chi squared distribution in addition the goodness of fit test is applied to test whether the model assumption is satisfied the corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion we evaluate the finite sample performance of the proposed procedures with monte carlo simulation studies the proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome aids data set

modeling of hormone secretion generating mechanisms with splines a pseudo likelihood approach a flexible and robust approach is proposed for the investigation of underlying hormone secretion generating mechanisms characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by slow decay we model hormone concentration as a filtered counting process where the intensity function of the counting process is modeled nonparametrically using periodic splines the intensity function and parameters are estimated using a combination of weighted least squares and pseudo likelihood based on the first two moments our method uses concentration measurements directly which avoids the difficult task of estimating pulse numbers and locations both simulations and applications suggest that our method performs well for estimating the intensity function of the pulse generating counting processes

nonparametric estimation of the variogram and its spectrum in the study of intrinsically stationary spatial processes a new nonparametric variogram estimator is proposed through its spectral representation the methodology is based on estimation of the variogram s spectrum by solving a regularized inverse problem through quadratic programming the estimated variogram is guaranteed to be conditionally negative definite simulation shows that our estimator is flexible and generally has smaller mean integrated squared error than the parametric estimator under model misspecification our methodology is applied to a spatial dataset of decadal temperature changes copyright 2011 oxford university press

smoothing spline anova for multivariate bernoulli observations with application to ophthalmology data we combine a smoothing spline analysis of variance ss anova model and a log linear model to build a partly flexible model for multivariate bernoulli data the joint distribution conditioning on the predictor variables is estimated the log odds ratio is used to measure the association between outcome variables a numerical scheme based on the block one step successive over relaxation sor newton ralphson algorithm is proposed to obtain an approximate solution for the variational problem we extend the generalized approximate cross validation gacv and the randomized gacv for choosing smoothing parameters to the case of multivariate bernoulli responses the randomized version is fast and stable to compute and is used to adaptively select smoothing parameters in each block onestep sor iteration approximate bayesian confidence intervals are obtained for the flexible estimates of the conditional logit functions simulation studies are conducted to check the performance of the proposed method using the com

functional principal component regression and functional partial least squares regression of a scalar response on signal predictors such as near infrared nir spectra of chemical samples presents a major challenge when as is typically the case the dimension of the signals far exceeds their number most solutions to this problem reduce the dimension of the predictors either by regressing on components e g principal component regression pcr and partial least squares pls or by smoothing methods which restrict the coefficient function to the span of a spline basis this article introduces functional versions of pcr and pls which combine both of the foregoing dimension reduction approaches two versions of functional pcr are developed both using b splines and roughness penalties the regularized components version applies such a penalty to the construction of the principal components i e it uses functional principal components whereas the regularized regression version incorporates a penalty in the regression for the latter form of functional pcr the penalty parame

shape invariant modeling of circadian rhythms with random effects and smoothing spline anova decompositions medical studies often collect physiological and or psychological measurements over time from multiple subjects to study dynamics such as circadian rhythms under the assumption that the expected response functions of all subjects are the same after shift and scale transformations shape invariant models have been applied to analyze this kind of data the shift and scale parameters provide efficient and interpretable data summaries while the common shape function is usually modeled nonparametrically to provide flexibility however due to the deterministic nature of the shift and scale parameters potential correlations within a subject are ignored furthermore the shape of the common function may depend on other factors such as disease in this article we propose shape invariant mixed effects models a second stage model with fixed and random effects is used to model individual shift and scale parameters a second stage smoothing spline anova model is used to study potential covariate effects on the common shape function we apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol a hormone that is affected by stress we find that patients with cushing s syndrome lost circadian rhythms and their 24 hour means were elevated to very high levels patients with major depression had the same circadian shape and phases as normal subjects however their 24 hour mean levels were elevated and amplitudes were dampened for some patients

semi parametric latent process model for longitudinal ordinal data application to cognitive decline ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies we propose a semi parametric model for the analysis of the change over time of such data in longitudinal studies a threshold model is defined where the outcome value depends on the current value of an underlying gaussian latent process the latent process model is a gaussian linear mixed model with a non parametric function of time f t to model the expected change over time this model includes random effects and a stochastic error process to flexibly handle correlation between repeated measures the function f t and all the model parameters are estimated by penalized likelihood using a cubic spline approximation for f t the smoothing parameter is estimated by an approximate cross validation criterion confidence bands may be computed for the estimated curves for the latent process and using a monte carlo approach for the outcome in its natural scale the method is applied to the paquid cohort data to compare the time course over 14 years of two cognitive scores in a sample of 350 future alzheimer patients and in a matched sample of healthy subjects

selecting the smoothing parameter for estimation of slowly changing evoked potential signals summary brain evoked potential ep data consist of a true response signal and random background activity noise which are observed over repeated stimulus presentations trials a signal that changes slowly from trial to trial can be estimated by smoothing across trials and over time within trials we present a method for selecting the smoothing parameter by minimizing an estimate of the mean average squared error mase we evaluate the performance of this method using simulated ep data and apply the method to an example set of real flash evoked potentials

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

interior w 2 p estimates for solutions of the monge ampere equation in this work we adapt the techniques developed in c1 to prove interior estimates for solutions of perturbations of the monge ampere equation

penalized likelihood approach to estimate a smooth mean curve on longitudinal data this paper aims to propose a penalized likelihood approach to estimate a smooth mean curve for the evolution with time of a gaussian variable taking into account the correlation structure of longitudinal data the model is an extension of the mixed effects linear model including an unspecified function of time f t the estimator f t is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic m spline with a reduced number of knots we present modifications of four criteria cross validation generalized cross validation t of rice akaike s criterion to estimate the smoothing parameter when data are correlated these four criteria gave very similar results in the simulation study the simulation study showed also the superiority of the bayesian confidence bands of the mean curve over the frequentist ones we develop empirical bayes estimates of subject specific deviations this approach was applied to study the progression of cd4 lymphocyte counts in a cohort of hiv patients treated with protease inhibitors copyright 2002 john wiley sons ltd

the regularity of mappings with a convex potential in this work we apply the techniques developed in cl to the problem of mappings with a convex potential between domains that is given two bounded domains q q2 of rn and two nonnegative real functions fi defined in qi that are bounded away from zero and infinity we want to study the map vf v w for a lipschitz convex v such that v maps ql onto q 2 in the a e sense and in some weak sense 1 f2 vyv det dij v f1 x in recent work y brenier showed existence and uniqueness of such a map provided that jaqil 0 under the obvious compatibility condition

regression splines in the time dependent coefficient rates model for recurrent event data many epidemiologic studies involve the occurrence of recurrent events and much attention has been given for the development of modeling techniques that take into account the dependence structure of multiple event data this paper presents a time dependent coefficient rates model that incorporates regression splines in its estimation procedure such methods would be appropriate in situations where the effect of an exposure or covariates changes over time in recurrent event data settings the finite sample properties of the estimators are studied via simulation using data from a randomized community trial that was designed to evaluate the effect of vitamin a supplementation on recurrent diarrheal episodes in small children we model the functional form of the treatment effect on the time to the occurrence of diarrhea the results describe how this effect varies over time in summary we observed a major impact of the vitamin a supplementation on diarrhea after 2 months of the dosage with the effect diminishing after the third dosage the proposed method can be viewed as a flexible alternative to the marginal rates model with constant effect in situations where the effect of interest may vary over time

bootstrap based inference on the difference in the means of two correlated functional processes we propose nonparametric inference methods on the mean difference between two correlated functional processes we compare methods that 1 incorporate different levels of smoothing of the mean and covariance 2 preserve the sampling design and 3 use parametric and nonparametric estimation of the mean functions we apply our method to estimating the mean difference between average normalized power of sleep electroencephalograms for 51 subjects with severe sleep apnea and 51 matched controls in the first 4 h after sleep onset we obtain data from the sleep heart health study the largest community cohort study of sleep although methods are applied to a single case study they can be applied to a large number of studies that have correlated functional data copyright 2012 john wiley sons ltd

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

streamlined variance calculations for semiparametric mixed models semiparametric mixed model analysis benefits from variability estimates such as standard errors of effect estimates and variability bars to accompany curve estimates we show how the underlying variance calculations can be done extremely efficiently compared with the direct naive approach these streamlined calculations are linear in the number of subjects representing a two orders of magnitude improvement

a frequency domain selection criterion for regression with autocorrelated errors abstract we consider the regression model yt t e t t 0 1 n 1 where y t are scalar observations t is the unknown regression function and e t are unobservable errors generated by a zero mean weakly stationary process independent of t and with completely unknown autocorrelation structure we propose a data driven method for selecting a parametric or nonparametric estimator of t the method is based on cross validation in the frequency domain and requires no assumptions about the form of the estimator or the error correlations it does however require the discrete fourier transform dft of the signal t to be a smooth complex function of frequency as is the case for example with transient signals or growth and decay curves after giving some general motivations for the method we focus on the special case of linear estimators of a nonparametric regression function including both kernel and spline estimators for these estimators we develop efficient methods of evaluating t

a note on penalized spline smoothing with correlated errors we investigate the behavior of data driven smoothing parameters for penalized spline regression in the presence of correlated data it has been shown for other smoothing methods that mean squared error minimizers such as generalized cross validation or the akaike information criterion are extremely sensitive to misspecifications of the correlation structure resulting in over or under fitting the data in contrast to this we show that a maximum likelihood based choice of the smoothing parameter is more robust and that for a moderately misspecified correlation structure over or under fitting does not occur this is demonstrated in simulations and data examples and is supported by theoretical investigations

inference of time varying regression models we consider parameter estimation hypothesis testing and variable selection for partially time varying coefficient models our asymptotic theory has the useful feature that it can allow dependent nonstationary error and covariate processes with a two stage method the parametric component can be estimated with a n 1 2 convergence rate a simulation assisted hypothesis testing procedure is proposed for testing significance and parameter constancy we further propose an information criterion that can consistently select the true set of significant predictors our method is applied to autoregressive models with time varying coefficients simulation results and a real data application are provided

optimal geostatistical model selection in many fields of science predicting variables of interest over a study region based on noisy data observed at some locations is an important problem two popular methods for the problem are kriging and smoothing splines the former assumes that the underlying process is stochastic whereas the latter assumes it is purely deterministic kriging performs better than smoothing splines in some situations but is outperformed by smoothing splines in others however little is known regarding selecting between kriging and smoothing splines in addition how to perform variable selection in a geostatistical model has not been well studied in this article we propose a general methodology for selecting among arbitrary spatial prediction methods based on approximately unbiased estimation of mean squared prediction errors using a data perturbation technique the proposed method accounts for estimation uncertainty in both kriging and smoothing spline predictors and is shown to be optimal in terms of two mean sq

semiparametric regression of multidimensional genetic pathway data least squares kernel machines and linear mixed models we consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least squares kernel machines lskms this unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way this semiparametric model also makes it possible to test for the overall genetic pathway effect we show that the lskm semiparametric regression can be formulated using a linear mixed model estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software both the regression coefficients of the covariate effects and the lskm estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation the smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood a score test is developed to test for the genetic pathway effect model variable selection within the lskm framework is discussed the methods are illustrated using a prostate cancer data set and evaluated using simulations

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

computational error bounds for laplace transform inversion based on smoothing splines abstract in the numerical methods for the laplace transform inversion the errors quantification in computational processes is a crucial issue in this paper we propose two inversion methods based on smoothing splines combined with a procedure for the derivation of error bounds in particular we numerically study the impact of the fitting error amplification through the analysis of several sources of error and their propagation

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

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

nonparametric profile monitoring by mixed effects modeling in some applications the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables profile monitoring is for checking the stability of this relationship over time control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically most existing control charts in the literature are for monitoring parametric profiles they require the assumption that within profile measurements are independent of each other which is often invalid in practice this article focuses on nonparametric profile monitoring when within profile data are correlated a novel control chart is suggested which incorporates local linear kernel smoothing into the exponentially weighted moving average ewma control scheme in this method within profile correlation is described by a nonparametric mixed effects model our proposed control chart is fast to compute and convenient to use numeric

the performance of cross validation and maximum likelihood estimators of spline smoothing parameters abstract an important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter in this article we report on an extensive simulation study that investigates the finite sample performance of generalized cross validation cross validation and marginal likelihood estimators of the smoothing parameter in splines of orders 2 and 3 the performance criterion for both the estimate of the function and its first derivative is measured by the square root of integrated squared error marginal likelihood using splines of degree 5 emerges as an attractive alternative to the other estimators in that it usually outperforms them and is also faster to compute

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

smoothing spline analysis of variance models a new tool for the analysis of cyclic biomechanical data cyclic biomechanical data are commonplace in orthopedic rehabilitation and sports research where the goal is to understand and compare biomechanical differences between experimental conditions and or subject populations a common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications and then comparing mean differences at specific points of the cycle this pointwise analysis approach ignores the functional nature of the data which can hinder one s ability to find subtle differences between experimental conditions and or subject populations to overcome this limitation we propose using mixed effects smoothing spline analysis of variance ssanova to analyze differences in cyclic biomechanical data the ssanova framework makes it possible to decompose the estimated function into the portion that is common across groups i e the average cycle ac and the portion that differs across groups i e the contrast cycle cc by partitioning the signal in such a manner we can obtain estimates of the cc differences ccds which are the functions directly describing group differences in the cyclic biomechanical data using both simulated and experimental data we illustrate the benefits of using ssanova models to analyze differences in noisy biomechanical gait signals collected from multiple locations joints of subjects participating in different experimental conditions using bayesian confidence intervals the ssanova results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and or subject populations

smoothing spline anova models for large data sets with bernoulli observations and the randomized gacv we propose the randomized generalized approximate cross validation rangacv method for choosing multiple smoothing parameters in penalized likelihood estimates for bernoulli data the method is intended for application with penalized likelihood smoothing spline anova models in addition we propose a class of approximate numerical methods for solving the penalized likelihood variational problem which in conjunction with the rangacv method allows the application of smoothing spline anova models with bernoulli data to much larger data sets than previously possible these methods are based on choosing an approximating subset of the natural representer basis functions for the variational problem simulation studies with synthetic data including synthetic data mimicking demographic risk factor data sets is used to examine the properties of the method and to compare the approach with the grkpack code of wang 1997c bayesian confidence intervals are obtained for the fits and are shown in the simulation studies to have the across the function property usually claimed for these confidence intervals finally the method is applied to an observational data set from the beaver dam eye study with scientifically interesting results

semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles summary we consider semiparametric regression for periodic longitudinal data parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect the within subject correlation is modeled using subject specific random effects and a random stochastic process with a periodic variance function we use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function whose estimator is shown to be a periodic cubic smoothing spline we use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components we show that all model parameters can be easily obtained by fitting a linear mixed model a common problem in the analysis of longitudinal data is to compare the time profiles of two groups e g between treatment and placebo we develop a scaled chi squared test for the equality of two nonparametric time functions the proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

hamiltonian constructions of kahler einstein metrics and kahler metrics of constant scalar curvature assuming the existence of a real torus acting through holomorphic isometries on a kahler manifold we construct an ansatz for kahler einstein metrics and an ansatz for kahler metrics with constant scalar curvature using this hamiltonian approach we solve the differential equations in special cases and find in particular a family of constant scalar curvature kahler metrics describing a non linear superposition of the bergman metric the calabi metric and a higher dimensional generalization of the lebrun kahler metric the superposition contains kahler einstein metrics and all the geometries are complete on the open disk bundle of some line bundle over the complex projective spacepn we also build such kahler geometries on kahler quotients of higher cohomogeneity

nonlinear stability of strong planar rarefaction waves for the relaxation approximation of conservation laws in several space dimensions abstract in this paper we show that a strong planar rarefaction wave is nonlinear stable namely it is an attractor for the relaxation approximation of the scalar conservation laws in several space dimensions compared with former results obtained by t p liu 1987 comm math phys 108 153 175 and t luo 1997 j differential equations 133 255 279 our main novelty lies in the fact that the planar rarefaction waves do not need to be small and in the one dimensional case the initial disturbance can also be chosen arbitrarily large

a localization property of viscosity solutions to the monge ampere equation and their strict convexity the purpose of this note is to show a localization property of convex viscosity solutions to the monge ampere inequality 0 1 2 n are strictly convex

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

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

nonparametric spline regression with autoregressive moving average errors summary we estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model unknown parameters are estimated by either maximum likelihood cross validation or generalized cross validation by expressing the problem in state space form we obtain 0 n algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross validation functions the finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given

skill luck and streaky play on the pga tour in this study we implement a random effects model that estimates cubic spline based time dependent skill functions for 253 active pga tour golfers over the 1998 2001 period our model controls for the first order autocorrelation of residual 18 hole scores and adjusts for round course and player course random effects using the model we are able to estimate time varying measures of skill and luck for each player in the sample estimates of spline based player specific skill functions provide strong evidence that the skill levels of pga tour players change through time using the model we are able to rank golfers at the end of 2001 on the basis of their estimated mean skill levels and identify the players who experienced the most improvement and deterioration in their skill levels over the 1998 2001 period we find that some luck is required to win pga tour events even for the most highly skilled players player course interactions contribute very little to variability in golfer performance but the par

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

on analyzing circadian rhythms data using nonlinear mixed models with harmonic terms summarywang ke and brown 2003 biometrics59 804 812 developed a smoothing based approach for modeling circadian rhythms with random effects their approach is flexible in that fixed and random covariates can affect both the amplitude and phase shift of a nonparametrically smoothed periodic function in motivating their approach wang et al stated that a simple sinusoidal function is too restrictive in addition they stated that although adding harmonics can improve the fit it is difficult to decide how many harmonics to include in the model and the results are difficult to interpret we disagree with the notion that harmonic models cannot be a useful tool in modeling longitudinal circadian rhythm data in this note we show how nonlinear mixed models with harmonic terms allow for a simple and flexible alternative to wang et al s approach we show how to choose the number of harmonics using penalized likelihood to flexibly model circadian rhythms and to estimate the effect of covariates on the rhythms we fit harmonic models to the cortisol circadian rhythm data presented by wang et al to illustrate our approach furthermore we evaluate the properties of our procedure with a small simulation study the proposed parametric approach provides an alternative to wang et al s semiparametric approach and has the added advantage of being easy to implement in most statistical software packages

dynamic conditionally linear mixed models for longitudinal data we develop a new class of models dynamic conditionally linear mixed models for longitudinal data by decomposing the within subject covariance matrix using a special cholesky decomposition here dynamic means using past responses as covariates and conditional linearity means that parameters entering the model linearly may be random but nonlinear parameters are nonrandom this setup offers several advantages and is surprisingly similar to models obtained from the first order linearization method applied to nonlinear mixed models first it allows for flexible and computationally tractable models that include a wide array of covariance structures these structures may depend on covariates and hence may differ across subjects this class of models includes e g all standard linear mixed models antedependence models and vonesh carter models second it guarantees the fitted marginal covariance matrix of the data is positive definite we develop methods for bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited

ricci flat metrics harmonic forms and brane resolutions we discuss the geometry and topology of the complete non compact ricci flat stenzel metric on the tangent bundle of s n 1 we obtain explicit results for all the metrics and show how they can be obtained from first order equations derivable from a superpotential we then provide an explicit construction for the harmonic self dual p q forms in the middle dimension p q n 1 for the stenzel metrics in 2 n 1 dimensions only the p p forms are l 2 normalisable while for p q forms the degree of divergence grows with we also construct a set of ricci flat metrics whose level surfaces are u 1 bundles over a product of n einstein kahler manifolds and we construct examples of harmonic forms there as an application we construct new examples of deformed supersymmetric non singular m2 branes with such 8 dimensional transverse ricci flat spaces we show explicitly that the fractional d3 branes on the 6 dimensional stenzel metric found by klebanov and strassler is supported by a pure 2 1 form and thus it is supersymmetric while the example of pando zayas tseytlin is supported by a mixture of 1 2 and 2 1 forms we comment on the implications for the corresponding dual field theories of our resolved brane solutions

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

semiparametric model building for regression models with time varying parameters abstract this paper considers the problem of semiparametric model building for linear regression models with potentially time varying coefficients by allowing the response variable and explanatory variables be jointly a nonstationary process the proposed methods are widely applicable to nonstationary and dependent observations we propose a local linear shrinkage method that can simultaneously achieve parameter estimation and variable selection its selection consistency and the favorable oracle property are established due to the fear of losing efficiency an information criterion is further proposed for distinguishing between time varying and time constant components numerical examples are presented to illustrate the proposed methods

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

generalized linear mixed models with varying coefficients for longitudinal data the routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects we relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time with random effects used to model the correlation induced by among subject and within subject variation due to the usually intractable integration involved in evaluating the quasi likelihood function the double penalized quasi likelihood dpql approach of lin and zhang 1999 journal of the royal statistical society series b61 381 400 is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects a scaled chi squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree we evaluate the performance of the procedures through simulation studies and illustrate their application with indonesian children infectious disease data

rarefactions and large time behavior for parabolic equations and monotone schemes we consider the large time behavior of monotone semigroups associated with degenerate parabolic equations and monotone difference schemes for an appropriate class of initial data the solution is shown to converge to rarefaction waves at a determined asymptotic rate

smoothing spline anova for exponential families with application to the wisconsin epidemiological study of diabetic retinopathy the 1994 neyman memorial lecture let y i i 1 n be independent observations with the density of y i of the form h y i f i exp y i f i b f i c y i where b and c are given functions and b is twice continuously differentiable and bounded away from 0 let i t f t i where t t 1 t d t 1 t d t the t are measurable spaces of rather general form and f is an unknown function on t with some assumed smoothness properties given y i t i i 1 n it is desired to estimate f t for t in some region of interest contained in t we develop the fitting of smoothing spline anova models to this data of the form f t c f t f t t the components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric anova the estimate of f is obtained as the minimizer in an appropriate function space of l y f j f j f where l y f is the negative log likelihood of y y 1 y n given f the j j are quadratic penalty functionals and the anova decomposition is terminated in some manner there are five major parts required to turn this program into a practical data analysis tool 1 methods for deciding which terms in the anova decomposition to include model selection 2 methods for choosing good values of the smoothing parameters 3 methods for making confidence statements concerning the estimate 4 numerical algorithms for the calculations and finally 5 public software in this paper we carry out this program relying on earlier work and filling in important gaps the overall scheme is applied to bernoulli data from the wisconsin epidemiologic study of diabetic retinopathy to model the risk of progression of diabetic retinopathy as a function of glycosylated hemoglobin duration of diabetes and body mass index it is believed that the results have wide practical application to the analysis of data from large epidemiologic studies

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

the estimation of branching curves in the presence of subject specific random effects branching curves are a technique for modeling curves that change trajectory at a change branching point currently the estimation framework is limited to independent data and smoothing splines are used for estimation this article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject if the branching point is modeled as a random effect then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model given existing issues with using random effects within a smoothing spline we express the model as a b spline based semiparametric nonlinear mixed effects model simple clever smoothness constraints are enforced on the b splines at the change point the method is applied to women s health data where we model the shape of the labor curve cervical dilation measured longitudinally before and after treatment with oxytocin a labor stimulant

semiparametric analysis of variance with tensor product thin plate splines we consider fitting multivariate models to response data based on analysis of variance anova like decompositions of functions of several variables f t 1 t d c f t f t t a theory for fitting some components of these models with polynomial smoothing splines exists when each t is in a subset of the real line in this case the various estimated components turn out to be certain tensor sums and products of polynomial splines this approach may not be natural when one or more of the variables are geographic in particular where nature does not know north from east

choice of bandwidth for kernel regression when residuals are correlated summary standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated in this paper we propose a modified version of an existing plug in bandwidth selector the method is generalized to stationary error variables by estimating a functional of the residual covariance function the proposed bandwidth selector shows good properties in asymptotic theory and in simulations without assuming a parametric model for the error process

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

local polynomial mixed effects models for longitudinal data we consider a nonparametric mixed effects model yi tij tij vi tij i tij j 1 2 ni i 1 2 n for longitudinal data we propose combining local polynomial kernel regression and linear mixed effects lme model techniques to estimate both fixedeffects population curve t and random effects curves vi t the resulting estimator called the local polynomial lme llme estimator takes the local correlation structure of the longitudinal data into account naturally we also propose new bandwidth selection strategies for estimating t and vi t simulation studies show that our estimator for t is superior to the existing estimators in the sense of mean squared errors the asymptotic bias variance mean squared errors and asymptotic normality are established for the llme estimators of t when ni is bounded and n tends to infinity our llme estimator converges in a standard nonparametric rate and the asymptotic bias and variance are essentially the same as those of the kernel generalized esti

inference in smoothing spline analysis of variance summary smoothing spline analysis of variance decomposes a multivariate function into additive components this decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0 no formal procedure is yet available to test such a hypothesis we propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0 this test allows us to choose an optimal model and to compare groups of curves we first develop the general theory by exploiting the connection between mixed effects models and smoothing splines we then apply this to compare two groups of curves and to select an optimal model in a two dimensional problem a small simulation is used to assess the finite sample performance of the likelihood ratio test