a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials this paper addresses the use of isogeometric analysis to solve solid mechanics problems involving nearly incompressible materials the present work is focused on extension of two field mixed variational formulations in both small and large strains to isogeometric analysis inf sup stable displacement pressure combinations for mixed formulations are developed based on the subdivision property of nurbs stability and convergence properties of the proposed displacement pressure combinations are illustrated by computing numerical inf sup constants and error norms the performance of the proposed formulations is assessed by studying several benchmark examples involving nearly incompressible and incompressible elastic and elasto plastic materials in both small and large strain regime

semiparametric transformation models for semicompeting survival data semicompeting risk outcome data e g time to disease progression and time to death are commonly collected in clinical trials however analysis of these data is often hampered by a scarcity of available statistical tools as such we propose a novel semiparametric transformation model that improves the existing models in the following two ways first it estimates regression coefficients and association parameters simultaneously second the measure of surrogacy for example the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint can be directly obtained we propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal extensive simulations demonstrate the valid usage of our method we apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients semicompeting outcomes namely time to progression and time to death

spectral correlations of fractional brownian motion fractional brownian motion fbm is a ubiquitous nonstationary model for many physical processes with power law time averaged spectra in this paper we exploit the nonstationarity to derive the full spectral correlation structure of fbm starting from the time varying correlation function we derive two different time frequency spectral correlation functions the ambiguity function and the kirkwood rihaczek spectrum and one dual frequency spectral correlation function the dual frequency spectral correlation has a surprisingly simple structure with spectral support on three discrete lines the theoretical predictions are verified by spectrum estimates of monte carlo simulations and of a time series of earthquakes with a magnitude of 7 and higher

a unified framework for fitting bayesian semiparametric models to arbitrarily censored survival data including spatially referenced data a comprehensive unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models proportional hazards proportional odds

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

isogeometric analysis of nearly incompressible solids this paper describes the use of isogeometric methods to solve problems in finite deformation solid mechanics in which compressible and nearly incompressible behavior may be encountered the work is based on a three field variational structures in which displacements mean stress and volume effects are independently approximated using this approach and tensor product nurbs approximations it is shown how the solution can be conducted in a standard approach where main variables are organized at nodes control points this leads to an efficient procedure to solve large problems of a general form without the need to develop special solution strategies the approach is demonstrated on some standard test problems copyright 2010 john wiley sons ltd

an energy stable mixed formulation for isogeometric analysis of incompressible hyper elastodynamics we develop a mixed formulation for incompressible hyper elastodynamics based on a continuum modeling framework recently developed in 41 and smooth generalizations of the taylor hood element based on non uniform rational b splines nurbs this continuum formulation draws a link between computational fluid dynamics and computational solid dynamics this link inspires an energy stability estimate for the spatial discretization which favorably distinguishes the formulation from the conventional mixed formulations for finite elasticity the inf sup condition is utilized to provide a bound for the pressure field the generalized method is applied for temporal discretization and a nested block preconditioner is invoked for the solution procedure 42 the inf sup stability for different pairs of nurbs elements is elucidated through numerical assessment the convergence rate of the proposed formulation with various combinations of mixed elements is examined by the manufactured solution method the numerical scheme is also examined under compressive and tensile loads for isotropic and anisotropic hyperelastic materials finally a suite of dynamic problems is numerically studied to corroborate the stability and conservation properties

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

peridynamic petrov galerkin method a generalization of the peridynamic theory of correspondence materials abstract the peridynamic petrov galerkin ppg method is a meshfree approach based on the peridynamic integro differential form of the momentum equation the spurious oscillations in the common peridynamic correspondence formulation are investigated they occur due to an inadmissible linearized mapping of the family deformation field this leads to a generalized correspondence formulation which contains the common formulation as a special case it is based on the weak form of the peridynamic momentum equation test and trial function requirements are examined which ensure an exact imposition of dirichlet and neumann boundary conditions and weighted least square wls shape functions as well as local maximum entropy lme approximants are utilized to examine the ppg method a consistent linearization is provided which can also be used to speed up common implicit peridynamic correspondence codes it is used in an implicit quasistatic framework to investigate the impact of different shape function combinations test cases show that low energy modes can be prevented by the ppg method and highlight the fast convergence and stability

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

a stabilised immersed boundary method on hierarchical b spline grids for fluid rigid body interaction with solid solid contact abstract an accurate efficient and robust numerical scheme is presented for the simulation of the interaction between flexibly supported rigid bodies and incompressible fluid flow with topology changes and solid solid contact the solution of the incompressible navier stokes equations is approximated by employing a stabilised formulation on cartesian grids discretised with hierarchical b splines the solid is modelled as a rigid body and represented by linear segments along its boundary kinematic conditions along the fluid rigid body interface are enforced weakly using nitsche s method while ghost penalty operators are employed to avoid excessive ill conditioning of the system matrix arising from small cut cells a staggered scheme is used for resolving the coupled fluid rigid body interaction the contact between moving or moving and fixed solid bodies is modelled with lagrange multipliers the excellent performance and wide range of applicability of the proposed scheme are demonstrated in a number of benchmark tests as well as industrially relevant model problems the examples cover the galloping phenomena particulate flow hydraulic check valves and a model turbine

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

brief paper stochastic tube mpc with state estimation an output feedback model predictive control mpc strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed given the probability distributions of the disturbance input the measurement noise and the initial state estimation error the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator from these distributions a set of deterministic constraints is computed for the predictions of a nominal model the constraints are incorporated in a receding horizon optimization of an expected quadratic cost which is formulated as a quadratic program the constraints are constructed so as to provide a guarantee of recursive feasibility and the closed loop system is stable in a mean square sense all uncertainties in this paper are taken to be bounded in most control applications this gives a more realistic representation of process and measurement noise than the more traditional gaussian assumption

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

simple random walk on long range percolation clusters ii scaling limits supported in part at the technion by a landau fellowship supported in part by an alfred sloan fellowship in mathematics

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

isogeometric analysis of nearly incompressible large strain plasticity abstract we study the behavior of nurbs based isogeometric analysis on problems of large deformation plasticity we evaluate the performance of standard nurbs elements and elements based on the f formulation of elguedj et al 2008 1 our experience shows that standard measures of evaluation employed in the literature namely displacements at selected locations and graphs of reaction forces versus displacements are often misleading metrics in problems of plasticity on the other hand stress distributions in the form of contour plots are in our experience revealing measure of element performance we also determine that the concept of mesh locking which has dominated investigations of low order elements is not a relevant issue for higher order nurbs elements for problems of large deformation plasticity however standard higher order nurbs elements of type qk of continuity class c k 1 k 2 typically exhibit spurious stress oscillations whereas the f elements of type qk qk 1 produce good results in all cases

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

time dependent cross ratio estimation for bivariate failure times in the analysis of bivariate correlated failure time data it is important to measure the strength of association among the correlated failure times one commonly used measure is the cross ratio motivated by cox s partial likelihood idea we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is examined using simulation studies and it is applied to the australian twin data

f bar based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids part i formulation and benchmarking this paper proposes a new technique which allows the use of simplex finite elements linear triangles in 2d and linear tetrahedra in 3d in the large strain analysis of nearly incompressible solids the new technique extends the f bar method proposed by de souza neto et al int j solids and struct 1996 33 3277 3296 and is conceptually very simple it relies on the enforcement of near incompressibility over a patch of simplex elements rather than the point wise enforcement of conventional displacement based finite elements within the framework of the f bar method this is achieved by assuming for each element of a mesh a modified f bar deformation gradient whose volumetric component is defined as the volume change ratio of a pre defined patch of elements the resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near incompressibility as the original f bar procedure the present methodology preserves the displacement based structure of the finite element equations as well as the strain driven format of standard algorithms for numerical integration of path dependent constitutive equations and can be used regardless of the constitutive model adopted the new elements are implemented within an implicit quasi static environment in this context a closed form expression for the exact tangent stiffness of the new elements is derived this allows the use of the full newton raphson scheme for equilibrium iterations the performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two and three dimensional numerical examples

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

isogeometric analysis of the isothermal navier stokes korteweg equations this paper is devoted to the numerical simulation of the navier stokes korteweg equations a phase eld model for water water vapor two phase ows we develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher order partial dierenti al operator that represents capillarity we introduce a new renement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions finally we present several numerical examples in two and three dimensions that illustrate the eectiveness and robustness of our approach

semiparametric normal transformation models for spatially correlated survival data there is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies in this article we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data this class of models assumes that survival outcomes marginally follow a cox proportional hazard model with unspecified baseline hazard and their joint distribution is obtained by transforming survival outcomes to normal random variables whose joint distribution is assumed to be multivariate normal with a spatial correlation structure a key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields we study the relationship of the spatial correlation structure of the transformed no

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

stability of higher order hood taylor methods the stability of a higher order hood taylor method for the approximation of the stationary stokes equations using continuous piecewise polynomials of degree 3 to approximate velocities and continuo

wavelet based parameter estimation for polynomial contaminated fractionally differenced processes we consider the problem of estimating the parameters for a stochastic process using a time series containing a trend component trend i e large scale variations in the series that are best modeled outside of a stochastic framework is often confounded with low frequency stochastic fluctuations this problem is particularly evident in models such as fractionally differenced fd processes which exhibit slowly decaying autocorrelations and can be extended to encompass nonstationary processes with substantial low frequency components we use the discrete wavelet transform dwt to estimate parameters for stationary and nonstationary fd processes in a model of polynomial trend plus fd noise using daubechies wavelet filters allows for automatic elimination of polynomial trends due to embedded differencing operations parameter estimation is based on an approximate maximum likelihood approach made possible by the fact that the dwt decorrelates fd processes approximately we consider this decorrelation in detail examining the between and within scale wavelet correlations separately better between scale decorrelation can be achieved by increasing the length of the wavelet filter whereas the within scale correlations can be handled via explicit modeling by a low order autoregressive process we demonstrate our methodology by applying it to a popular climate dataset

jackknifing linear estimating equations asymptotic theory and applications in stochastic processes let x1 x2 x be a vector of possibly dependent random variables having distribution f x 0 let g x 0 e 1 gi x 0 0 be an estimating equation for 0 e g the score function or the maximum pseudolikelihood estimating equation in spatial processes let o n be the estimator obtained from g such that 0on 0o in probability and n 1 2 0 00 n o v in distribution in many situations it is difficult to derive an analytical expression for v e g for maximum pseudolikelihood estimators for the spatial processes in this paper we give a jackknife estimator of v and show that it is weakly consistent the method consists of deleting one estimating equation instead of one observation at a time and thus obtaining the pseudovalues the method of proof and conditions are similar to those of reeds with some modifications the method applies equally to independent and identically distributed random variables independent but not identically distributed random variables timeor space dependent stochastic processes our conditions are less severe than carlstein s who deals with a similar problem of estimating v for dependent observations we also give some simulation results

asymptotic theory for the frailty model the frailty model is a generalization of cox s proportional hazards model which includes a random effect nielsen gill andersen and sorensen 1992 proposed an em algorithm to estimate the cumulative baseline hazard and the variance of the random effect here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

mixed stress displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity abstract we propose a mixed stress displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von mises plasticity the discretization is based on isogeometric analysis iga with non uniform rational b splines nurbs as basis functions as compared to conventional iga galerkin formulations isogeometric collocation methods offer a high potential of computational cost reduction for higher order discretizations as they eliminate the need for quadrature in the proposed mixed formulation both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues which occur in displacement based isogeometric collocation for nearly incompressible elasticity and von mises plasticity the performance of the proposed approach is demonstrated by several numerical examples

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

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

composite likelihood bayesian information criteria for model selection in high dimensional data for high dimensional data sets with complicated dependency structures the full likelihood approach often leads to intractable computational complexity this imposes difficulty on model selection given that most traditionally used information criteria require evaluation of the full likelihood we propose a composite likelihood version of the bayes information criterion bic and establish its consistency property for the selection of the true underlying marginal model our proposed bic is shown to be selection consistent under some mild regularity conditions where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size simulation studies demonstrate the empirical performance of this new bic especially for the scenario where the number of parameters increases with sample size technical proofs of our theoretical results are provided in the online supplemental materials

tempered stable levy motion driven by stable subordinator a b s t r a c t in this article we propose a new model for financial data description combining two independent mechanisms namely the tempered stable process and inverse stable subordinator we obtain a new model which captures not only the tempered stable character of the underlying data but also such a property as periods in which the values of an asset stay on the same level moreover we classify our system to the family of subdiffusive processes and investigate its tail behavior we describe in detail testing and estimation procedures for the proposed model in the last step we calibrate our model to the real data

erratum to a stochastic controller for a scalar linear system with additive cauchy noise automatica 50 1 2014 114 127 abstract a stochastic control scheme is developed for scalar discrete time and linear dynamic systems driven by cauchy distributed process and measurement noises when addressing the optimal control problem for such systems the standard quadratic cost criteria cannot be used in this study we introduce a new objective function that is functionally similar to the cauchy probability density function the performance index defined as the expectation of this objective function with respect to the cauchy densities exists the dynamic programming solution to the fixed and finite horizon optimal control problem that uses this performance index appears to be intractable therefore a moving horizon optimal model predictive control problem is implemented for which the conditional expected value of the objective function and its gradients can be computed in closed form and without assumptions such as certainty equivalence numerical results are shown for this m step model predictive optimal controller and compared to a similar linear exponential gaussian model predictive controller an essential difference between the cauchy and gaussian controllers when applied to a system with cauchy noises is that while the gaussian controller is linear and reacts strongly to all noise pulses the cauchy controller can differentiate between measurement and process noise pulses by ignoring the former while responding to the latter this property of the cauchy controller occurs when an impulsive measurement noise is more likely than an impulsive process noise the cauchy and gaussian controllers react similarly when applied to a system with gaussian noises demonstrating the robustness of the proposed control scheme

prediction of spatial cumulative distribution functions using subsampling abstract the spatial cumulative distribution function scdf is a random function that provides a statistical summary of a random field over a spatial domain of interest in this article we develop a spatial subsampling method for predicting an scdf based on observations made on a hexagonal grid similar to the one used in the environmental monitoring and assessment program of the u s environmental protection agency we show that under quite general conditions the proposed subsampling method provides accurate data based approximations to the sampling distributions of various functionals of the scdf predictor in particular it produces estimators of different population characteristics such as the quantiles and weighted mean integrated squared errors of the empirical predictor as an illustration we apply the subsampling method to construct large sample prediction bands for the scdf of an ecological index for foliage condition of red maple trees in the state of maine

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data we consider a class of semiparametric normal transformation models for right censored bivariate failure times nonparametric hazard rate models are transformed to a standard normal model and a joint normal distribution is assumed for the bivariate vector of transformed variates a semiparametric maximum likelihood estimation procedure is developed for estimating the marginal survival distribution and the pairwise correlation parameters this produces an efficient estimator of the correlation parameter of the semiparametric normal transformation model which characterizes the bivariate dependence of bivariate survival outcomes in addition a simple positive mass redistribution algorithm can be used to implement the estimation procedures since the likelihood function involves infinite dimensional parameters the empirical process theory is utilized to study the asymptotic properties of the proposed estimators which are shown to be consistent asymptotically normal and semiparametric efficient a simple estimator for the variance of the estimates is also derived the finite sample performance is evaluated via extensive simulations

nurbs based least squares finite element methods for fluid and solid mechanics summary this contribution investigates the performance of a least squares finite element method based on non uniform rational b splines nurbs basis functions the least squares functional is formulated directly in terms of the strong form of the governing equations and boundary conditions thus the introduction of auxiliary variables is avoided but the order of the basis functions must be higher or equal to the order of the highest spatial derivatives the methodology is applied to the incompressible navier stokes equations and to linear as well as nonlinear elastic solid mechanics the numerical examples presented feature convective effects and incompressible or nearly incompressible material the numerical results which are obtained with equal order interpolation and without any stabilisation techniques are smooth and accurate it is shown that for p and h refinement the theoretical rates of convergence are achieved copyright 2014 john wiley sons ltd

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

a stabilised immersed boundary method on hierarchical b spline grids abstract in this work an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b spline grid and employs the non symmetric and penalty free version of nitsche s method to enforce the boundary conditions the strategy allows for h and p refinement and employs a so called ghost penalty term to stabilise the cut cells an effective procedure based on hierarchical subdivision and sub cell merging which avoids excessive numbers of quadrature points is used for the integration of the cut cells a basic laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty free nitsche method as well as their impact on accuracy the methodology is also applied to the incompressible navier stokes equations where the supg pspg stabilisation is employed simulations of the lid driven cavity flow and the flow around a cylinder at low reynolds number show the good performance of the methodology excessive ill conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

a general resampling scheme for triangular arrays of alpha mixing random variables with application to the problem of spectral density estimation in 1989 kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the m dimensional joint distribution of stationary and alpha mixing observations the modification amounts to resampling whole blocks of consecutive observations or deleting whole blocks one at a time liu and singh independently proposed in 1988 the same technique for observations that are m dependent however many time series statistics notably estimators of the spectral density function involve parameters of the whole infinite dimensional joint distribution and hence do not fit in this framework in this report we generalize the moving blocks resampling scheme of kunsch and liu and singh a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution we then apply this result to the problem of estimation of the spectral density

spatial extended hazard model with application to prostate cancer survival summary this article develops a bayesian semiparametric approach to the extended hazard model with generalization to high dimensional spatially grouped data county level spatial correlation is accommodated marginally through the normal transformation model of li and lin 2006 journal of the american statistical association 101 591 603 using a correlation structure implied by an intrinsic conditionally autoregressive prior efficient markov chain monte carlo algorithms are developed especially applicable to fitting very large highly censored areal survival data sets per variable tests for proportional hazards accelerated failure time and accelerated hazards are efficiently carried out with and without spatial correlation through bayes factors the resulting reduced interpretable spatial models can fit significantly better than a standard additive cox model with spatial frailties

characteristic functions of random variables attracted to 1 stable laws the domain of attraction of a 1 stable law on r d is characterized by the expansions of the characteristic functions of its elements

locking free finite element methods for linear and nonlinear elasticity in 2d and 3d abstract the uniform convergence of finite element approximations based on a modified hu washizu formulation for the nearly incompressible linear elasticity is analyzed we show the optimal and robust convergence of the displacement based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements these choices include bases that are well known as well as newly constructed bases starting from a suitable three field problem we extend our dependent three field formulation to geometrically nonlinear elasticity with saint venant kirchhoff law additionally an dependent three field formulation for a general hyperelastic material model is proposed a range of numerical examples using different material laws for small and large strain elasticity is presented

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

mixtures of polya trees for flexible spatial frailty survival modelling mixtures of polya trees offer a very flexible nonparametric approach for modelling time to event data many such settings also feature spatial association that requires further sophistication either at the point level or at the lattice level in this paper we combine these two aspects within three competing survival models obtaining a data analytic approach that remains computationally feasible in a fully hierarchical bayesian framework using markov chain monte carlo methods we illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the surveillance epidemiology and end results program of the national cancer institute our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions ignore spatial association or both

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects