a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

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

robust autoregressive estimates using quadratic programming abstract the robust estimation of the autoregressive parameters is formulated in terms of the quadratic programming problem this article s main contribution is to present an estimator that down weights both types of outliers in time series and improves the forecasting results new robust estimates are yielded by combining optimally two weight functions suitable for innovation and additive outliers in time series the technique which is developed here is based on an approach of mathematical programming applications to ip approximation the behavior of the estimators are illustrated numerically under the additive outlier generating model monte carlo results show that the proposed estimators compared favorably with respect to m estimators and bounded influence estimators based on these results we conclude that one can improve the robust properties of ar p estimators using quadratic programming

likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative summary for submodels of an exponential family we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable first we establish the asymptotic equivalence between the likelihood ratio test and the score test secondly the score test representation is used to derive the asymptotic distribution of the likelihood ratio test these results are derived for general submodels of an exponential family without assuming compactness of the parameter space we then exemplify the results on a class of multivariate normal models where null hypotheses concerning the covariance structure lead to loss of identifi ability of a parameter our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation

robust and consistent estimates of autoregressive moving average parameters summary we aim at estimates of autoregressive moving average parameters which are simultaneously consistent at the nominal gaussian model and insensitive to outliers in the data the estimates may be viewed as a robust version of maximum likelihood estimates of order r and for purely autoregressive models reduce to a special case of generalized m estimates

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

consistency of the jackknife after bootstrap variance estimator for the bootstrap quantiles of a studentized statistic efron j roy statist soc ser b 54 1992 83 1111 proposed a computationally efficient method called the jackknife after bootstrap for estimating the variance of a bootstrap estimator for independent data for dependent data a version of the jackknife after bootstrap method has been recently proposed by lahiri econometric theory 18 2002 79 98 in this paper it is shown that the jackknife after bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data results from a simulation study are also presented

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

theoretical comparisons of block bootstrap methods in this paper we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths it is shown that asymptotically bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order however the variances of these bootstrap estimators may be different even in the first order expansions for the bias the variance and the mean squared error of different block bootstrap variance estimators are obtained it follows from these expansions that using overlapping blocks is to be preferred over nonoverlapping blocks and that using random block lengths typically leads to mean squared errors larger than those for nonrandom block lengths

analysis and improvements of global local enrichments for the generalized finite element method abstract partition of unity methods like the gfem rely on closed form analytical enrichment functions however only limited a priori knowledge about the solution is available for many problems of engineering relevance control of discretization errors in this class of problems requires mesh refinement which offsets some of the advantages associated with these methods this has led to the development of the gfem with global local enrichments gfem gl which uses ideas of the classical global local finite element method to numerically build enrichment functions for the gfem it involves the solution of local boundary value problems using boundary conditions from the solution of the global problem discretized with a coarse mesh these local solutions are in turn used to enrich the solution space of the global problem with the help of the partition of unity framework this paper presents an a priori error estimate accounting for the effect of inexact boundary conditions applied to local problems two strategies to control the error of the gfem gl solution due to these boundary conditions are also presented the first one is based on the use of a buffer or over sampling zone in the local problems the second strategy investigated is based on multiple global local iterations several numerical experiments performed on three dimensional fracture mechanics problems illustrate the effectiveness of these strategies in controlling the error of the gfem gl solution the problems are selected such that the boundary conditions on the local problems range from smooth to singular functions

asymptotics of some estimators and sequential residual empiricals in nonlinear time series this paper establishes the asymptotic uniform linearity of m and r scores in a family of nonlinear time series and regression models it also gives an asymptotic expansion of the standardized sequential residual empirical process in these models these results are in turn used to obtain the asymptotic normality of certain classes of m r and minimum distance estimators of the underlying parameters the classes of estimators considered include analogs of hodges lehmann huber and lad least absolute deviation estimators some applications to the change point and testing of the goodness of fit problems in threshold and amplitude dependent exponential autoregression models are also given the paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models

on principles for the selection of shape functions for the generalized finite element method abstract effective shape functions for the generalized finite element method should reflect the available information on the solution this information is partially fuzzy because the solution is of course unknown and typically the only available information is the solution s inclusion in a variety of function spaces it is desirable to choose shape functions that perform robustly over a family of relevant situations quantitative notions of robustness are introduced and discussed we show in particular that in one dimension polynomials are robust when the available information consists in inclusions in sobolev type spaces that are x independent

reml estimation asymptotic behavior and related topics the restricted maximum likelihood reml estimates of dispersion parameters variance components in a general non normal mixed model are defined as solutions of the reml equations in this paper we show the reml estimates are consistent if the model is asymptotically identifiable and infinitely informative under the location invariant class and are asymptotically normal a n if in addition the model is asymptotically nondegenerate the result does not require normality or boundedness of the rank p of design matrix of fixed effects moreover we give a necessary and sufficient condition for asymptotic normality of gaussian maximum likelihood estimates mle in non normal cases as an application we show for all unconfounded balanced mixed models of the analysis of variance the reml anova estimates are consistent and are also a n provided the models are nondegenerate the mle are consistent a n if and only if certain constraints on p are satisfied

qualitative robustness for stochastic processes in this paper we generalize hampel s concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non i i d observations defining appropriate metrics between samples we also present a different approach to qualitative robustness which formalizes the notion of resistance we give two definitions based on this approach strong and weak resistance we show that for estimating a finite dimensional real parameter pi robustness is equivalent to weak resistance and in the i i d case is also equivalent to strong resistance finally we prove the strong resistance of a class of estimators which includes common gm estimates for linear models and autoregressive processes

a particle partition of unity method for the solution of elliptic parabolic and hyperbolic pdes in this paper we present a meshless discretization technique for instationary convection diffusion problems it is based on operator splitting the method of characteristics and a generalized partition of unity method we focus on the discretization process and its quality the method may be used as an h version or a p version even for general particle distributions the convergence behavior of the different versions corresponds to that of the respective version of the finite element method on a uniform grid we discuss the implementational aspects of the proposed method furthermore we present the results of numerical examples where we considered instationary convection diffusion instationary diffusion linear advection and elliptic problems

quasi optimal rates of convergence for the generalized finite element method in polygonal domains we consider a mixed boundary value interface problem for the elliptic operator p i j i a i j j u f on a polygonal domain r 2 with straight sides we endowed the boundary of partially with dirichlet boundary conditions u 0 on d and partially with neumann boundary conditions i j i a i j j u 0 on n the coefficients a i j are piecewise smooth with jump discontinuities across the interface which is allowed to have singularities and cross the boundary of in particular we consider triple junctions and even multiple junctions our main result is to construct a sequence of generalized finite element spaces s n that yield h m quasi optimal rates of convergence m 1 for the galerkin approximations u n s n of the solution u more precisely we prove that u u n c dim s n m 2 f h m 1 where c depends on the data for the problem but not on f u or n and dim s n our construction is quite general and depends on a choice of a good sequence of approximation spaces s n on a certain subdomain w that is at some distance to the vertices in case the spaces s n are generalized finite element spaces then the resulting spaces s n are also generalized finite element spaces

robust estimates for arma models abstract two new classes of robust estimates for arma models are introduced estimates based on residual autocovariances ra estimates and estimates based on truncated residual autocovariances tra estimates a heuristic derivation of the asymptotic normal distribution is given we also perform a monte carlo study to compare the robustness properties of these estimates with the least squares m and gm estimates in this study we consider observations that correspond to a gaussian model with additive outliers the monte carlo results show that ra and tra estimates compare favorably with respect to least squares m and gm estimates

a particle partition of unity method part ii efficient cover construction and reliable integration in this paper we present a meshfree discretization technique based only on a set of irregularly spaced points x i in mathbb r d and the partition of unity approach in this sequel to m griebel and m a schweitzer siam j sci comput 22 2000 pp 853 890 we focus on the cover construction and its interplay with the integration problem arising in a galerkin discretization we present a hierarchical cover construction algorithm and a reliable decomposition quadrature scheme here we decompose the integration domains into disjoint cells on which we employ local sparse grid quadrature rules to improve computational efficiency the use of these two schemes already reduces the operation count for the assembly of the stiffness matrix significantly now the overall computational costs are dominated by the number of the integration cells we present a regularized version of the hierarchical cover construction algorithm which reduces the number of integration cells even further and subsequently improves the computational efficiency in fact the computational costs during the integration of the nonzeros of the stiffness matrix are comparable to that of a finite element method yet the presented method is completely independent of a mesh moreover our method is applicable to general domains and allows for the construction of approximations of any order and regularity

edgeworth expansions for studentized statistics under weak dependence in this paper we derive valid edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process under dependence the asymptotic variance of such a statistic is given by an infinite series oflag covariances and therefore studentizing factors i e estimators of the asymptotic standard error typically involve an increasing number say l of lag covariance estimators which are themselves quadratic functions of the observations the unboundedness of the dimension l of these quadratic functions makes the derivation and the form of the expansions nonstandard it is shown that in contrast to the case of the studentized means under independence the derived edgeworth expansion is a superposition of three distinct series respectively given by one in powers of n 1 2 one in powers of n l 1 2 resulting from the standard error of the studentizing factor and one in powers of the bias of the studentizing factor where n denotes the sample size

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

a nonconforming generalized finite element method for transmission problems we obtain quasi optimal rates of convergence for transmission interface problems on domains with smooth curved boundaries using a nonconforming generalized finite element method gfem more precisely we study the strongly elliptic problem pu sum partial j a ij partial i u f in a smooth bounded domain omega with dirichlet boundary conditions the coefficients a ij are piecewise smooth possibly with jump discontinuities along a smooth closed surface gamma called the interface which does not intersect the boundary of the domain we consider a sequence of approximation spaces s mu satisfying two conditions 1 nearly zero boundary and interface matching and 2 approximability which are similar to those in babuska nistor and tarfulea j comput appl math 218 2008 pp 175 183 then if u mu in s mu mu ge 1 is a sequence of galerkin approximations of the solution u to the interface problem the approximation error u u mu hat h 1 omega is

improving the rate of convergence of high order finite elements on polygons and domains with cusps let u and uv v be the solution and respectively the discrete solution of the non homogeneous dirichlet problem u f on u 0 for any m and any bounded polygonal domain we provide a construction of a new sequence of finite dimensional subspaces vn such that where f hm 1 is arbitrary and c is a constant that depends only on and not on n we do not assume u hm 1 the existence of such a sequence of subspaces was first proved in a ground breaking paper by babuska 8 our method is different it is based on the homogeneity properties of sobolev spaces with weights and the well posedness of non homogeneous dirichlet problem in suitable sobolev spaces with weights for which we provide a new proof and which is a substitute of the usual shift theorems for boundary value problems in domains with smooth boundary our results extended right away to domains whose boundaries have conical points we also indicate some of the changes necessary to deal with domains with cusps our numerical computation are in agreement with our theoretical results

meshfree particle methods for thin plates abstract in this paper we are concerned with meshfree particle methods for the solutions of the classical plate model the vertical displacement of a thin plate is governed by a fourth order elliptic equation and thus the approximation functions for numerical solutions are required to have continuous partial derivatives hence the conventional finite element method has difficulties to solve the fourth order problems meshfree methods have the advantage of constructing smooth approximation functions however most of the earlier works on meshfree methods for plate problems used either moving least squares method with penalty method or coupling fem with meshfree method to deal with essential boundary conditions in this paper by using generalized product partition of unity introduced by oh et al we introduce meshfree particle methods in which approximation functions have high order polynomial reproducing property and the kronecker delta property we also prove error estimates for the proposed meshfree methods moreover to demonstrate the effectiveness of our method results of the proposed method are compared with existing results for various shapes of plates with variety of boundary conditions and loads

robustness analysis of the phase phase correlator to white impulsive noise with applications to autoregressive modeling using only the phase information and a relationship based on the gaussian hypergeometric function the phase phase correlator can be utilized to estimate the normalized cross correlation coefficient between two zero mean complex gaussian processes this estimator naturally introduces a certain robustness to white impulsive observation noise over the gaussian maximum likelihood estimator this correspondence examines the robustness of the phase phase correlator in the presence of uncorrelated impulsive noise we show that its asymptotic bias compares favorably to the robust schweppe type gm estimator with the huber function termed shgm at a cost of efficiency application of the ppc to autoregressive time series analysis is illustrated with a parametric spectral estimation example

general m estimates for contaminated p th order autoregressive processes consistency and asymptotic normality this work is concerned with simultaneous estimation of coefficients and a scale parameter of a p th order autoregressive process x t the observations are y t v t z t 1 v t x t where z t is a contaminating process and v t represents the proportion of contamination if x t or z t have heavy tails both least squares estimates and ordinary m estimates are seriously affected under general conditions we prove consistency and asymptotic normality of a general class of m estimates which contains some m estimates studied by denby and martin 6

blockwise bootstrapped empirical process for stationary sequences we apply the bootstrap for general stationary observations proposed by kunsch to the empirical process for p dimensional random vectors it is known that the empirical process in the multivariate case converges weakly to a certain gaussian process we show that the bootstrapped empirical process converges weakly to the same gaussian process almost surely assuming that the block length l for constructing bootstrap replicates satisfies l n o n 1 2 varepsilon 0 varepsilon frac 1 2 and l n rightarrow infty an example where the multivariate setup arises are the robust gm estimates in an autoregressive model we prove the asymptotic validity of the bootstrap approximation by showing that the functional associated with the gm estimates is frechet differentiable

the change of variance function for dependent data the infinitesimal stability of the asymptotic variance is considered form estimators of a location parameter when the nominal sample with i i d data is contaminated by a possibly dependent process it is shown that the resulting change of variance function can be expressed as a sum of two terms one corresponding contamination of the univariate distribution and one to contamination of the bivariate distributions a change of variance sensitivity is introduced the form of which is closely related to the average patch length of the outliers finally optimalv robust and mostv robust score functions are derived the resulting family of estimators is the same as for independent data in the general case but the truncation point approaches zero when dependency is accounted for for redescending score functions the family of estimators is changed

tests for genetic linkage and homogeneity this report concerns likelihood ratio tests in a heterogeneous model for linkage where the recombination fraction has a binomial mixture distribution with an unknown proportion of unlinked families we consider families of unequal sizes with known or unknown phase data in both cases the limit distributions of the linkage test statistics are a mixture of a mass at and of a x2 1 distribution in equal proportions and homogeneity test statistics tend to the supremum of gaussian processes the critical values of the homogeneity tests are simulated and the power functions of the linkage and homogeneity tests are compared in a simulation study

analysis and applications of a generalized finite element method with global local enrichment functions abstract this paper presents a procedure to build enrichment functions for partition of unity methods like the generalized finite element method and the hp cloud method the procedure combines classical global local finite element method concepts with the partition of unity approach it involves the solution of local boundary value problems using boundary conditions from a global problem defined on a coarse discretization the local solutions are in turn used to enrich the global space using the partition of unity framework the computations at local problems can be parallelized without difficulty allowing the solution of large problems very efficiently the effectiveness of the approach in terms of convergence rates and computational cost is investigated in this paper we also analyze the effect of inexact boundary conditions applied to local problems and the size of the local domains on the accuracy of the enriched global solution key aspects of the computational implementation in particular the numerical integration of generalized fem approximations built with global local enrichment functions are presented the method is applied to fracture mechanics problems with multiple cracks in the domain our numerical experiments show that even on a serial computer the method is very effective and allows the solution of complex problems our analysis also demonstrates that the accuracy of a global problem defined on a coarse mesh can be controlled using a fixed number of global degrees of freedom and the proposed global local enrichment functions

on the sharpness of certain local estimates for projections into finite element spaces influence of a re entrant corner in a plane polygonal domain with a reentrant corner consider a homogeneous dirichlet problem for poisson s equation au f with f smooth and the corresponding galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi uniform uniformly regular triangulations with the diameter of each element compara