a bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model when multicentre clinical trial data are analysed it has become more and more popular to look for possible heterogeneity in outcome between centres however beyond the investigation of such heterogeneity it is also interesting to consider heterogeneity in treatment effect over centres for time to event outcomes this may be investigated by including a random centre effect and a random treatment by centre interaction in a cox proportional hazards model assuming independence between the random effects we propose a bayesian approach to fit our proposed model the parameters of interest are the variance components sigma 0 2 and a of these random effects which can be interpreted as a measure of centre and treatment effect over centres heterogeneity of the hazard these variance components are estimated from their marginal posterior density after integrating out the fixed treatment effect and the random effects as this integration cannot be performed analytically the marginal posterior density is approximated using the laplace integration technique statistical inference is then based on the characteristics of the posterior marginal density such as the mode and the standard deviation we demonstrate the proposed technique using data from a pooled database of seven eortc bladder cancer clinical trials substantial centre and treatment effect over centres heterogeneity in disease free interval was found copyright c 2005 john wiley sons ltd

fixed smoothing asymptotics for time series 1 in this paper we derive higher order edgeworth expansions for the finite sample distributions of the subsampling based t statistic and the wald statistic in the gaussian location model under the so called fixed smoothing paradigm in particular we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions the results are used to justify the second order correctness of a new bootstrap method the gaussian dependent bootstrap in the context of gaussian location model 1 introduction many economic and financial applications involve time series data with autocorrelation and heteroskedasticity properties often the unknown dependence structure is not the chief object of interest but the inference on the parameter of interest involves the estimation of unknown dependence in stationary time series models estimated by generalized method of moments gmm robust inference is typically accomplished by consistently estimating the asymptotic covariance matrix which is proportional to the long run variance lrv matrix of the estimating equations or moment conditions defining the estimator using a kernel smoothing method in the econometrics and statistics literature the bandwidth parameter truncation lag involved in the kernel smoothing method is assumed to grow slowly with sample size in order to achieve consistency the inference is conducted by plugging in a covariance matrix estimator that is consistent under heteroskedasticity and autocorrelation this approach dates back to newey and west 25 and andrews 1 recently kiefer and vogelsang 13 kv hereafter developed an alternative first order asymptotic theory for the hac heteroskedasticity and autocorrelation consistent based robust inference where the proportion of the bandwidth involved in the hac estimator to the sample size t denoted as b is held fixed in the asymptotics under the fixed b asymptotics the hac estimator converges to a nondegenerate yet nonstandard limiting distribution the tests based on the fi xed b asymptotic approximation were shown to enjoy better finite sample properties than the tests based on the small b asymptotic theory

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

a second order accurate symmetric discretization of the poisson equation on irregular domains in this paper we consider the variable coefficient poisson equation with dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple discretization moreover since our discretization matrix is symmetric it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second order accurate discretizations of this problem multidimensional computational results are presented to demonstrate the second order accuracy of this numerical method in addition we use our approach to formulate a second order accurate symmetric implicit time discretization of the heat equation on irregular domains then we briefly consider stefan problems

a smooth block bootstrap for quantile regression with time series quantile regression allows for broad conditional characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications because quantile regression estimators have complex limiting distributions several bootstrap methods for the independent data setting have been proposed many of which involve smoothing steps to improve bootstrap approximations currently no similar advances in smoothed bootstraps exist for quantile regression with dependent data to this end we establish a smooth tapered block bootstrap procedure for approximating the distribution of quantile regression estimators for time series this bootstrap involves two rounds of smoothing in resampling individual observations are resampled via kernel smoothing techniques and resampled data blocks are smoothed by tapering the smooth bootstrap results in performance improvements over previous unsmoothed versions of the block bootstrap as well as normal approximations based on powell s kernel variance estimator which are common in application our theoretical results correct errors in proofs for earlier and simpler versions of the unsmoothed moving blocks bootstrap for quantile regression and broaden the validity of block bootstraps for this problem under weak conditions we illustrate the smooth bootstrap through numerical studies and examples

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

a finite volume element formulation and error analysis for the non stationary conduction convection problem abstract the non stationary conduction convection problem including the velocity vector field and the pressure field as well as the temperature field is studied with a finite volume element fve method a fully discrete fve formulation and the error estimates between the fully discrete fve solutions and the accuracy solution are provided it is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions moreover it is shown that the fve method is feasible and efficient for finding the numerical solutions of the non stationary conduction convection problem and is one of the most effective numerical methods by comparing the results of the numerical simulations of the fve formulation with those of the numerical simulations of the finite element method and the finite difference scheme for the non stationary conduction convection problem

modeling multivariate survival data by a semiparametric random effects proportional odds model summary in this article the focus is on the analysis of multivariate survival time data with various types of dependence structures examples of multivariate survival data include clustered data and repeated measurements from the same subject such as the interrecurrence times of cancer tumors a random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model the distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log odds function this class of models which includes the usual shared random effects model the additive variance components model and the dynamic random effects model as special cases is highly flexible and is capable of modeling a wide range of multivariate survival data a unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal likelihood approach unlike the fully parametric case the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects the marginal likelihood is approximated by the monte carlo method simulation studies are carried out to investigate the performance of the proposed method the proposed method is applied to two well known data sets including clustered data and recurrent event times data

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

a reduced order extrapolated crank nicolson finite spectral element method based on pod for the 2d non stationary boussinesq equations abstract in this paper we mainly utilize proper orthogonal decomposition pod to reduce the order for the coefficient vector of the classical crank nicolson finite spectral element ccnfse method of the two dimensional 2d non stationary boussinesq equations about vorticity stream functions so that the reduced order method maintains all the advantages of the ccnfse method toward this end we first establish a ccnfse format with the second order time accuracy for the two dimensional 2d non stationary boussinesq equations about vorticity stream functions and analyze the existence stability and convergence of the ccnfse solutions and then by pod we establish a reduced order extrapolated crank nicolson finite spectral element roecnfse method and analyze the existence stability and convergence of the roecnfse solutions as well as offer the flowchart for seeking roecnfse solutions finally we use two sets of numerical experiments to validate that the numerical computational consequences are accorded with the theoretical ones such that the effectiveness and feasibility of the roecnfse method are further verified both theory and method in this paper is new and completely different from the existing reduced order methods

a reduced finite volume element formulation and numerical simulations based on pod for parabolic problems a proper orthogonal decomposition pod method is applied to a usual finite volume element fve formulation for parabolic equations such that it is reduced to a pod fve formulation with lower dimensions and high enough accuracy the error estimates between the reduced pod fve solution and the usual fve solution are analyzed it is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced pod fve formulation based on pod method is both feasible and highly efficient

fixed b subsampling and the block bootstrap improved confidence sets based on p value calibration summary subsampling and block based bootstrap methods have been used in a wide range of inference problems for time series to accommodate the dependence these resampling methods involve a bandwidth parameter such as the subsampling window width and block size in the block based bootstrap in empirical work using different bandwidth parameters could lead to different inference results but traditional first order asymptotic theory does not capture the choice of the bandwidth we propose to adopt the fixed b approach as advocated by kiefer and vogelsang in the heteroscedasticity auto correlation robust testing context to account for the influence of the bandwidth on inference under the fixed b asymptotic framework we derive the asymptotic null distribution of the p values for subsampling and the moving block bootstrap and further propose a calibration of the traditional small b based confidence intervals regions or bands and tests our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters such as the marginal distribution function simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts

a fully discrete stabilized mixed finite volume element formulation for the non stationary conduction convection problem abstract at first a semi discrete formulation with respect to time for the non stationary conduction convection problem is recalled then a fully discrete stabilized mixed finite volume element smfve formulation based on two local gauss integrals and parameter free is established directly from the semi discrete formulation with respect to time for the non stationary conduction convection problem following this the error estimates for the fully discrete smfve solutions are derived by means of the standard mixed finite element method finally some numerical experiments are presented illustrating that the numerical errors are consistent with theoretical results the degrees of freedom of the fully discrete smfve formulation are far fewer than those of the classical finite volume element fve formulation without any stabilization and its numerical solutions are more stable than those of the classical fve formulation without any stabilization thus validating that the fully discrete smfve formulation is feasible and efficient for finding the numerical solutions of the non stationary conduction convection problem

goodness of fit tests for conditional models under censoring and truncation the problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring a general method is applied to derive tests for the polynomial regression the proportional hazards the additive risks and the proportional odds models bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study

cubic superconvergent finite volume element method for one dimensional elliptic and parabolic equations in this paper a cubic superconvergent finite volume element method based on optimal stress points is presented for one dimensional elliptic and parabolic equations for elliptic problem it is proved that the method has optimal third order accuracy with respect to h 1 norm and fourth order accuracy with respect to l 2 norm we also obtain that the scheme has fourth order superconvergence for derivatives at optimal stress points for parabolic problem the scheme is given and error estimate is obtained with respect to l 2 norm finally numerical examples are provided to show the effectiveness of the method

a mixed finite volume element method based on rectangular mesh for biharmonic equations this paper presents a mixed finite volume element scheme based on rectangular partition for solving biharmonic equations it also gives a kind of adaptive uzawa iteration method for the scheme it is rigorously proved that the scheme has first order accuracy in h1 semi norm and l2 norm according to the characteristics of the scheme finally two numerical examples illustrate the effectiveness of the method

proper orthogonal decomposition based reduced order stabilized mixed finite volume element extrapolating model for the nonstationary incompressible boussinesq equations abstract in this study we employ a proper orthogonal decomposition pod method to establish a pod based reduced order stabilized mixed finite volume element smfve extrapolating model with very few degrees of freedom for the nonstationary incompressible boussinesq equations we provide error estimates of the pod based reduced order smfve solutions and the algorithm implementation for the pod based reduced order smfve extrapolating model in addition we present some numerical experiments that verify the validity and reliability of the pod based reduced order smfve extrapolating model

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

superconvergent biquadratic finite volume element method for two dimensional poisson s equations in this paper a kind of biquadratic finite volume element method is presented for two dimensional poisson s equations by restricting the optimal stress points of biquadratic interpolation as the vertices of control volumes the method can be effectively implemented by alternating direction technique it is proved that the method has optimal energy norm error estimates the superconvergence of numerical gradients at optimal stress points is discussed and it is proved that the method has also superconvergence displacement at nodal points by a modified dual argument technique finally a numerical example verifies the theoretical results and illustrates the effectiveness of the method

additive hazards model with multivariate failure time data summary marginal additive hazards models are considered for multivariate survival data in which individuals may experience events of several types and there may also be correlation between individuals estimators are proposed for the parameters of such models and for the baseline hazard functions the estimators of the regression coefficients are shown asymptotically to follow a multivariate normal distribution with a sandwich type covariance matrix that can be consistently estimated the estimated baseline and subject specific cumulative hazard processes are shown to converge weakly to a zero mean gaussian random field the weak convergence properties for the corresponding survival processes are established a resampling technique is proposed for constructing simultaneous confidence bands for the survival curve of a specific subject the method ology is extended to a multivariate version of a class of partly parametric additive hazards model simulation studies are conducted to assess finite sample properties and the method is illustrated with an application to development of coronary heart diseases and cardiovascular accidents in the framingham heart study

a reduced order extrapolation algorithm based on sfve method and pod technique for non stationary stokes equations in this paper a reduced order extrapolation algorithm roea based on proper orthogonal decomposition pod technique and classical stabilized finite volume element sfve method for non stationary stokes equations is established the error estimates between the roea solutions and the classical sfve solutions and the implementation for solving roea are provided some numerical examples are used to verify that the results of numerical computation are consistent with theoretical conclusions moreover it is shown that roea based on sfve formulation and pod method is feasible and efficient for solving non stationary stokes equations

analysis of the cell centred finite volume method for the diffusion equation abstract this paper presents a rigorous theoretical analysis of the cell centred finite volume method for poisson s equation we review the traditional taylor series expansion technique which suggests that the cell centred method is inconsistent on nonuniform grids which is not confirmed by numerical experiments we then present an analysis of the method which confirms that the solution error does indeed reduce as the cell size is reduced this is supported by numerical calculations

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

analysis of covariance with incomplete data via semiparametric model transformations we propose a method for fitting semiparametric models such as the proportional hazards ph additive risks ar and proportional odds po models each of these semiparametric models implies that some transformation of the conditional cumulative hazard function at each t depends linearly on the covariates the proposed method is based on nonparametric estimation of the conditional cumulative hazard function forming a weighted average over a range of t values and subsequent use of least squares to estimate the parameters suggested by each model an approximation to the optimal weight function is given this allows semiparametric models to be fitted even in incomplete data cases where the partial likelihood fails e g left censoring right truncation however the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the ph or any of the other semiparametric models in fact we propose an integrated method for data analysis where the role of the various semiparametric models is to suggest the best fitting transformation a single continuous covariate and several categorical covariates factors are allowed simulation studies indicate that the test statistics and confidence intervals have good small sample performance a real data set is analyzed

fitting conditional survival models to meta analytic data by using a transformation toward mixed effects models frailty models are widely used to model clustered survival data classical ways to fit frailty models are likelihood based we propose an alternative approach in which the original problem of fitting a frailty model is reformulated into the problem of fitting a linear mixed model using model transformation we show that the transformation idea also works for multivariate proportional odds models and for multivariate additive risks models it therefore bridges segregated methodologies as it provides a general way to fit conditional models for multivariate survival data by using mixed models methodology to study the specific features of the proposed method we focus on frailty models based on a simulation study we show that the proposed method provides a good and simple alternative for fitting frailty models for data sets with a sufficiently large number of clusters and moderate to large sample sizes within covariate level subgroups in the clusters the proposed method is applied to data from 27 randomized trials in advanced colorectal cancer which are available through the meta analysis group in cancer

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

a node centered local refinement algorithm for poisson s equation in complex geometries this paper presents a method for solving poisson s equation with dirichlet boundary conditions on an irregular bounded three dimensional region the method uses a nodal point discretization and adaptive mesh refinement amr on cartesian grids and the amr multigrid solver of almgren the discrete laplacian operator at internal boundaries comes from either linear or quadratic shortley weller extrapolation and the two methods are compared it is shown that either way solution error is second order in the mesh spacing error in the gradient of the solution is first order with linear extrapolation but second order with shortley weller examples are given with comparison with the exact solution the method is also applied to a heavy ion fusion accelerator problem showing the advantage of adaptivity

the product limit estimator and the bootstrap some asymptotic representations the product limit estimator and its quantile process are represented as i i d mean processes with a remainder of ordern 3 4 logn 3 4 a s corresponding bootstrap versions of these representations are given which can help one visualize how the bootstrap procedure operates in this set up

a reduced order crank nicolson finite volume element formulation based on pod method for parabolic equations in this paper a proper orthogonal decomposition pod method is used to deal with a classical crank nicolson finite volume element cnfve method for two dimensional parabolic equations a reduced order cnfve formulation with lower dimensions and sufficiently high accuracy based on pod technique is established the error estimates between reduced order cnfve solutions based on the pod method and classical cnfve solutions are provided and the extrapolation algorithm for solving reduced order cnfve formulation is implemented some numerical examples show that the results of numerical computation are consistent with previous theoretical conclusions moreover it is shown that the reduced order cnfve formulation based on pod method is feasible and efficient for solving two dimensional parabolic equations

analysis of a cell vertex finite volume method for convection diffusion problems a cell vertex finite volume approximation of elliptic convection dominated diffusion equations is considered in two dimensions the scheme is shown to be stable and second order convergent in a mesh dependent l 2 norm

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

a reduced fve formulation based on pod method and error analysis for two dimensional viscoelastic problem abstract proper orthogonal decomposition pod method has been successfully used in the reduced order modeling of complex systems in this paper we extend the applications of pod method i e combine a classical finite volume element fve method with pod method to establish a reduced fve formulation with lower dimensions and sufficiently high accuracy for two dimensional viscoelastic problem with real practical applied background and analyze the errors between the reduced pod fve solution and the classical fve solution so as to provide scientific theoretic basis for service applications some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced fve formulation based on pod method is feasible and efficient for solving two dimensional viscoelastic problem

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field