influence functions of iteratively reweighted least squares estimators abstract the iteratively reweighted least squares algorithm is routinely employed to evaluate robust regression estimates the importance of beginning the algorithm with a robust estimator of the unknown parameters is often stressed the precise influence of the initial estimator on subsequent iterates or the limit of such estimators however does not seem to have been calculated previously because robust regression involves the downweighting of specific points having large rescaled residuals and or large leverages in the design space it is natural to think in terms of the weights themselves rather than some less intuitive function such as the function of generalized m estimators therefore we consider multiple linear regression by the method of weighted least squares where the weights are estimated quantities depending on both position in the design space and the residual relative to an initial regression estimator the influence function of the weighted least squares estimator is shown to depend

implementation of a generalized exponential basis functions method for linear and non linear problems this is the accepted version of the following article mossaiby f ghaderian m rossi r implementation of a generalized exponential basis functions method for linear and non linear problems international journal for numerical methods in engineering on line jul 2015 which has been published in final form at http dx doi org 10 1002 nme 4985

a green s discrete transformation meshfree method for simulating transient diffusion problems this manuscript presents the formulation and application of the green s discrete transformation method gdtm for the meshfree simulation of transient diffusion problems including those with moving boundaries the gdtm implements a linear combination of time dependent green s basis functions defined on a set of source points to approximate the field in the form of a solution series a discrete transformation is implemented to evaluate unknown coefficients of this series which eliminates the need to use time integration schemes we will study the optimal number and location of the gdtm source points that yield the highest level of accuracy while maintaining a manageable condition number for the resulting linear system of equations the optimal values of these parameters which are inherently independent of the domain geometry are determined such that the basis functions have appropriate features for approximating the field a comprehensive convergence study is presented to show the precision and convergence rate of the gdtm for modeling various diffusion problems we also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies heat transfer in a turbine blade thermal response of a porous material and localized pitting corrosion in stainless steel copyright c 2015 john wiley sons ltd

bootstrapping a regression equation some empirical results abstract the bootstrap like the jackknife is a technique for estimating standard errors the idea is to use monte carlo simulation based on a nonparametric estimate of the underlying error distribution the main object of this article is to present the bootstrap in the context of an econometric equation describing the demand for energy by industry as it turns out the conventional asymptotic formulas for estimating standard errors are too optimistic by factors of nearly three when applied to a particular finite sample problem in a simpler context this finding can be given a mathematical proof

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

censored quantile regression with partially functional effects quantile regression offers a flexible approach to analyzing survival data allowing each covariate effect to vary with quantiles in practice constancy is often found to be adequate for some covariates in this paper we study censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects such a model can offer a simpler view regarding covariate survival association and moreover can enable improvement in estimation efficiency we propose profile estimating equations and present an iterative algorithm that can be readily and stably implemented asymptotic properties of the resultant estimators are established a simple resampling based inference procedure is developed and justified extensive simulation studies demonstrate efficiency gains of the proposed method over a naive two stage procedure the proposed method is illustrated via an application to a recent renal dialysis study

stability and convergence of the method of fundamental solutions for helmholtz problems on analytic domains the method of fundamental solutions mfs is a popular tool to solve laplace and helmholtz boundary value problems its main drawback is that it often leads to ill conditioned systems of equations in this paper we investigate for the interior helmholtz problem on analytic domains how the singularities charge points of the mfs basis functions have to be chosen such that approximate solutions can be represented by the mfs basis in a numerically stable way for helmholtz problems on the unit disc we give a full analysis which includes the high frequency short wavelength limit for more difficult and nonconvex domains such as crescents we demonstrate how the right choice of charge points is connected to how far into the complex plane the solution of the boundary value problem can be analytically continued which in turn depends on both domain shape and boundary data using this we develop a recipe for locating charge points which allows us to reach error norms of typically 10 1 1 on a wide variety of analytic domains at high frequencies of order only 3 points per wavelength are needed which compares very favorably to boundary integral methods

hermitian harmonic maps from complete hermitian manifolds to complete riemannian manifolds in this paper we study a nonlinear elliptic system of equations imposed on a map from a complete hermitian non kahler manifold to a riemannian manifold this system is more appropriate to hermitian geometry than the harmonic map system since it is compatible with the holomorphic structure of the domain manifold in the sense that holomorphic maps are hermitian harmonic maps it was first studied by jost and yau in j y and was applied to study the rigidity of compact hermitian manifolds we extend their existence and uniqueness results to the case where both domain and target manifolds are complete hopefully the results will be useful to study corresponding rigidity of complete hermitian manifolds let m be a complex manifold with hermitian metric h and let n be a riemannian manifold with metric gij and christoffel symbols i jk a hermitian harmonic map u m n satisfies the following elliptic system

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

generalization of robustness test procedure for error estimators part i formulation for patches near kinked boundaries in this part of paper we shall extend the formulation proposed by babuska and co workers for robustness patch test for quality assessment of error estimators to more general cases of patch locations especially in three dimensional problems this is performed first by finding an asymptotic finite element solution at interior parts of a problem with assumed smooth exact solution and then adding a correction part to obtain the solution near a kinked boundary irrespective of other boundary conditions at far ends of the domain it has been shown that the solution corresponding to the correction part may be obtained in a spectral form by assuming a suitable proportionality relation between the nodal values of a mesh with repeatable pattern of macro patches having found the asymptotic finite element solution the performance of error estimators may be examined although in this paper we focus on the asymptotic behaviour of error estimators the method described in this part may be used to obtain finite element solution for two three dimensional unbounded heat elasticity problems with homogeneous differential equations some numerical results are presented to show the validity and performance of the proposed method copyright 2005 john wiley sons ltd

dynamic solution of unbounded domains using finite element method discrete green s functions in frequency domain in this paper we present a new approach for finite element solution of time harmonic wave problems on unbounded domains as representatives of the wave problems discrete green s functions are evaluated in finite element sense the finite element mesh is considered to be of repeatable pattern cell constructed in rectangular co ordinates the system of fe equations is therefore reduced to a set of well known dispersion equations by using a spectral solution approach the spectral wave bases are constructed directly from the fe dispersion equations radiation condition is satisfied by selecting the wave bases so that the wave information is transmitted in appropriate directions at the cell level dirichlet neumann boundary conditions are defined at the edges of a quadrant of the main domain while using the axes of symmetry of the problem a new discrete transformation method recently proposed by the authors is used to satisfy the boundary conditions comprehensive studies are made for showing the validity accuracy and convergence of the solutions the results of the benchmark problems indicate that the proposed method can be used to evaluate discrete green s functions whose analytical forms are not available

construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order in this paper a novel method is presented to construct singular basis functions for solving harmonic and bi harmonic problems with weak singularities such bases are found without any knowledge of the singularity order the singular bases are constructed by choosing a series as a tensor product of chebyshev polynomials and trigonometrical functions in radial and angular directions respectively and applying weak form of the governing equation with such features the singular bases are categorized as the equilibrated basis functions the constructed singular functions can be utilized as a complementary part to the smooth part of the approximation in the solution of problems with singularities to demonstrate the efficiency of employing such singular bases they are used in a boundary node method through the solution of some examples selected from the well known literature the capability of the method is shown it will be demonstrated that the main function and its derivatives are excellently approximated at very close neighborhood of the singular point the method may especially be found useful for those who research on the extended finite element method or similar ideas

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

convergence of unsymmetric kernel based meshless collocation methods this paper proves convergence of variations of the unsymmetric kernel based collocation method introduced by kansa in 1986 since then this method has been very successfully used in many applications though it may theoretically fail in special situations and though it had no error bound or convergence proof up to now thus it is necessary to add assumptions or to make modifications our modifications prevent numerical failure by dropping strict collocation and allow a rigorous mathematical analysis proving error bounds and convergence rates these rates improve with the smoothness of the solution the domain and the kernel providing the trial spaces but they are currently not yet optimal and deserve refinement they are based on rates of approximation to the residuals by nonstationary meshless kernel based trial spaces and they are independent of the type of differential operator the results are applicable to large classes of linear problems in strong form provided that there is a smooth solution and the test and trial discretizations are chosen with some care our analysis does not require assumptions like ellipticity and it can be extended to ill posed problems

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

mallows type bounded influence regression trimmed means abstract the influence functions of the regression trimmed mean estimators proposed by koenker and bassett 1978 and welsh 1987 are bounded in the dependent variable space but not in the independent variable space this article follows the approach of mallows 1973 1975 and modifies these estimators so that the resulting estimators have bounded influence functions the large sample behavior of these estimators is studied and it is shown that they have the same asymptotic distribution the small sample behaviors of the ordinary regression and bounded influence regression trimmed means are then investigated by means of a monte carlo study and by applying the estimators to water salinity data see ruppert and carroll 1980 based on these results we conclude that one can potentially gain much by using bounded influence regression trimmed means over ordinary regression trimmed means however there does not seem to be a clear choice between the koenker bassett and welsh versions

benchmarks in nonlocal elasticity defined by eringen s integral model abstract in this paper we present low residual approximate solutions for nonlocal 1d and 2d elasticity problems defined according to eringen s integral model the benchmarks in the 1d cases are defined by prescribing the stress field while the unknown fields are the strains or the displacements for the 2d cases we define problems with equilibrated tractions and evaluate the approximate displacement field meanwhile a fourier series as well as a set of chebyshev polynomials are used as the basis functions for the main unknown fields we increase the number of the approximation functions to decrease the norm of the residuals and repeat the procedure until reasonable accuracy is obtained for the final solution since the procedure is very time consuming in some benchmark problems we present the calculated coefficients and in some other we give some point wise values for further use the results presented in this paper are particularly useful for the validation and convergence studies when numerical methods are to be used for the solution of the nonlocal elasticity problems

one step l estimators for the linear model we propose and investigate the asymptotic properties of a class of estimators of the regression parameter in the general linear model the estimators depend on a preliminary estimate of the regression parameter and the residuals based on it for the location model the estimators are linear combinations of the order statistics and the robustness and efficiency properties of this class of estimators carry over to the general linear model the estimators settle the doubts raised by bickel 1973 about the feasibility of the construction of a general class of reparametrization invariant estimators of a regression parameter which are linear combinations of order statistics in the location problem

the generalized finite element method for helmholtz equation part ii effect of choice of handbook functions error due to absorbing boundary conditions and its assessment abstract in part i t strouboulis i babuska r hidajat the generalized finite element method for helmholtz equation theory computation and open problems comput methods appl mech engrg 195 2006 4711 4731 we introduced the q version of the generalized finite element method gfem for the helmholtz equation and we addressed its a pollution error due to the wave number b exponential q convergence c robustness to perturbations of the mesh the roundoff and numerical quadrature errors and d a posteriori error estimation here we continue the development of the gfem for helmholtz and we address the effects of a alternative handbook functions and mesh types b the error due to the artificial truncation boundary conditions and its assessment the conclusions are 1 the employment of plane wave wave band and vekua handbook functions lead to equivalent results and 2 for high q the most significant component of error may be the one due to the artificial truncation boundary conditions a rather straightforward approach for assessing this error is proposed

exponential basis functions in solution of incompressible fluid problems with moving free surfaces in this paper a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries a lagrangian formulation established on pressure as a potential equation is employed in this method the approximate solution is expressed by a linear combination of exponential basis functions ebfs with complex valued exponents satisfying the governing equation constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique the numerical solution is performed in a time marching approach using an implicit algorithm in each time step the governing equation is solved at the beginning and the end of the step with the aid of an intermediate geometry the use of ebfs helps to find boundary velocities with high accuracy leading to a precise geometry updating the developed lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems non linear sloshing fluids in rigid rectangular two dimensional basins are particularly addressed

robustness in real life a study of clinical laboratory data previous studies have evaluated the performance of robust estimators of location using computer generated distributions this paper describes how distributions commonly seen in biomedical research differ from the simulated distributions and compares the performance of six families of estimators using samples from four biomedical distributions the biomedical distributions can be asymmetric and have shorter tails and other anomalies such as digit preferences which are not modeled in simulation studies the four biomedical distributions studied differ markedly from the models previously studied and these differences strongly affect the robust estimators in such situations the trimmed mean provides an improvement over the sample mean and its performance is more stable than that of estimators whose psi functions have steeply descending tails the central value and dispersion of each of the estimators are evaluated

the trimmed mean in the linear model pour le modele lineaire general a erreurs independantes on propose et on examine les proprietes de grands echantillons d un estimateur du parametre de regression

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

simple modifications for stabilization of the finite point method a stabilized version of the finite point method fpm is presented a source of instability due to the evaluation of the base function using a least square procedure is discussed a suitable mapping is proposed and employed to eliminate the ill conditioning effect due to directional arrangement of the points a step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution it is shown that the conventional version of fpm may lead to wrong results when the proposed mapping algorithm is not used it is shown that another source for instability and non monotonic convergence rate in collocation methods lies in the treatment of neumann boundary conditions unlike the conventional fpm in this work the neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods the stabilization procedure may be considered as an interpretation of the finite calculus fic method the main difference between the two stabilization procedures lies in choosing the characteristic length in fic and the weight of the boundary residual in the proposed method the new approach also provides a unique definition for the sign of the stabilization terms the reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared several numerical examples are presented to demonstrate the performance and convergence of the proposed methods copyright 2005 john wiley sons ltd

the method of fundamental solutions for inverse boundary value problems associated with the steady state heat conduction in anisotropic media in this paper the method of fundamental solutions is applied to solve some inverse boundary value problems associated with the steady state heat conduction in an anisotropic medium since the resulting matrix equation is severely ill conditioned a regularized solution is obtained by employing the truncated singular value decomposition while the optimal regularization parameter is chosen according to the l curve criterion numerical results are presented for both two and three dimensional problems as well as exact and noisy data the convergence and stability of the proposed numerical scheme with respect to increasing the number of source points and the distance between the fictitious and physical boundaries and decreasing the amount of noise added into the input data respectively are analysed a sensitivity analysis with respect to the measure of the accessible part of the boundary and the distance between the internal measurement points and the boundary is also performed the numerical results obtained show that the proposed numerical method is accurate convergent stable and computationally efficient and hence it could be considered as a competitive alternative to existing methods for solving inverse problems in anisotropic steady state heat conduction copyright 2005 john wiley sons ltd

a meshless method for unbounded acoustic problems in this paper an effective meshless method is proposed to solve time harmonic acoustic problems defined on unbounded domains to this end the near field is discretized by a set of nodes and the far field effect is taken into account by considering radiative boundary conditions the approximation within the near field is performed using a set of local residual free basis functions defined on a series of finite clouds for considering the far field effect a series of infinite clouds are defined on which another set of residual free bases satisfying the radiation conditions are considered for the approximation validation of the results is performed through solving some acoustic problems

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

special short wave elements for flow acoustics a numerical formulation based on the partition of unity method pum is proposed for modelling the propagation of short acoustic waves on irrotational mean flows the method seeks to reduce the pollution error which exists in conventional fe schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected helmholtz equation initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging diverging duct with mean flow next a simple two dimensional model of a straight duct with uniform flow is considered in both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and mach number characteristic of aero engine bypass ducts

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

a comparison of the variance estimation methods for heteroscedastic nonlinear models heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice we discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters the simulation study suggests that when the true variance is a function of the mean model the power of the mean variance function estimation method and the transform both sides method are the best choices for estimating the standard errors of the estimated model parameters in general the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias especially when the heterogeneity is nonsystematic across values of the covariate furthermore we note that the two modified sandwich estimators are appealing choices in practice considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform both sides approach copyright 2016 john wiley sons ltd

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

bootstrap confidence intervals for a class of parametric problems summary we consider the following class of problems having observed a multivariate normal data vector y with unknown mean vector q covariance matrix the identity find an approximate confidence interval for 0 t q a real valued function of q a simple geometric construction is given which leads to highly accurate solutions this construction shows that the standard approximation based on maximum likelihood theory 04 cz00 can be quite misleading when 0 is nonlinear in q we discuss bootstrap based confidence intervals which remove most of the error in the standard approximation at the expense of considerably more calculation the bootstrap intervals are invariant under transformation of both y and i and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality without requiring knowledge of the normalizing transformation

exponential basis functions in solution of static and time harmonic elastic problems in a meshless style in this paper exponential basis functions ebfs are used in a boundary collocation style to solve engineering problems whose governing partial differential equations pdes are of constant coefficient type complex valued exponents are considered for the ebfs two dimensional elasto static and time harmonic elasto dynamic problems are chosen in this paper the solution procedure begins with first finding a set of appropriate ebfs and then considering the solution as a summation of such ebfs with unknown coefficients the unknown coefficients are determined by the satisfaction of the boundary conditions through a collocation method with the aid of a consistent and complex discrete transformation technique the basis and various forms of the transformation have been addressed and discussed we shall propose several strategies for selection of ebfs with the aid of the basis explained for the transformation while using the transformation the number of ebfs should not necessarily be equal to or less than the number of boundary information data a library of ebfs has also been presented for further use the effect of body forces is included in the solution via construction of particular solution by the use of the discrete transformation and another series of ebfs a number of sample problems are solved to demonstrate the capabilities of the method it has been shown that the time harmonic problems with high wave number can be solved without much effort the method categorized in meshless methods can be applied to many other problems in engineering mechanics and general physics since ebfs can easily be found for almost all problems with constant coefficient pdes

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

a heteroskedasticity robust breusch pagan test for contemporaneous correlation in dynamic panel data models abstract this paper proposes a heteroskedasticity robust breusch pagan test of the null hypothesis of zero cross section or contemporaneous correlation in linear panel data models without necessarily assuming independence of the cross sections the procedure allows for either fixed strictly exogenous and or lagged dependent regressor variables as well as quite general forms of both non normality and heteroskedasticity in the error distribution the asymptotic validity of the test procedure is predicated on the number of time series observations t being large relative to the number of cross section units n in that either i n is fixed as t or ii n 2 t 0 as both t and n diverge jointly to infinity given this it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when t n is small because of this we also propose and establish asymptotic validity of a number of wild bootstrap schemes designed to provide improved inference when t n is small across a variety of experimental designs a monte carlo study suggests that the predictions from asymptotic theory do in fact provide a good guide to the finite sample behaviour of the test when t is large relative to n however when t and n are of similar orders of magnitude discrepancies between the nominal and empirical significance levels occur as predicted by the first order asymptotic analysis on the other hand for all the experimental designs the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels when t n is small with a recursive design wild bootstrap scheme performing best in general and providing quite close agreement between the nominal and empirical significance levels of the test even when t and n are of similar size moreover in comparison with the wild bootstrap version of the original breusch pagan test godfrey and yamagata 2011 our experiments indicate that the corresponding version of the heteroskedasticity robust breusch pagan test appears reliable as an illustration the proposed tests are applied to a dynamic growth model for a panel of 20 oecd countries

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

positivity conditions in meshless collocation methods collocation meshless methods are conceptually simple easy to implement and fast numerical methods the robustness of collocation methods has however been an issue especially for scattered set of points in this paper we show that the robustness of collocation meshless methods can be improved by ensuring that certain conditions defined as the positivity conditions are satisfied when constructing approximation functions and their derivatives the significance of positivity conditions is pointed out by an error analysis of the finite cloud method which is a collocation based meshless method we propose techniques based on modification of weighting functions to ensure satisfaction of positivity conditions on the approximation function and its derivatives when using a scattered set of points several types of weighting functions are tested for 1d and 2d problems on scattered points numerical results demonstrate the effectiveness of collocation methods when positivity conditions are satisfied

inference from stratified samples second order analysis of three methods for nonlinear statistics abstract for stratified samples and nonlinear statistics that can be expressed as functions of estimated totals second order asymptotic expansions of the linearization jackknife and balanced repeated replication variance estimators are obtained based on these comparisons are made in terms of their biases some higher order asymptotic equivalence results are also established the special case of a combined ratio estimator is investigated in detail some results on bias reduction achieved by the jack knife and balanced repeated replication estimators of a nonlinear function of totals are also given

robust permutation tests for correlation and regression coefficients abstractgiven a sample from a bivariate distribution consider the problem of testing independence a permutation test based on the sample correlation is known to be an exact level test however when used to test the null hypothesis that the samples are uncorrelated the permutation test can have rejection probability that is far from the nominal level further the permutation test can have a large type 3 directional error rate whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value when in fact the true correlation is negative it will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of type 1 or type 3 errors these conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution we will also present asymptotically robust randomization tests for regression coeffi

a bootstrap comparison of genetic covariance matrices summary an important problem in evolutionary biology is how population bottlenecks affect additive genetic variance va when only additive effects are present a decrease in va is predicted whereas with many forms of nonadditive interactions an increase is predicted we present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle tribolium castaneum in this experiment the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population the population then went through a bottleneck and the genetic covariance matrix was again measured these data were analyzed by first examining the univariate estimates for va and second examining the covariance matrices for the univariate measures the statistic we used was the change in va for the multivariate comparisons we used three measures the difference in rank the difference in the number of positive eigenvalues to test changes in the number of heritable traits a multivariate equivalent of bartlett s statistic to test changes in the size of the matrices and a modification of mantel s correlation to test for changes in the correlation structure of the matrices because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared we chose to use a bootstrap analysis to test for significance for females we found that following the population bottleneck va was significantly decreased and that the correlation structure of the matrix was significantly changed for males we found that following the population bottleneck va significantly increased but that the correlation structure was unchanged

the method of fundamental solutions for the cauchy problem in two dimensional linear elasticity in this paper the application of the method of fundamental solutions to the cauchy problem in two dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularised by employing the first order tikhonov functional while the choice of the regularisation parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries as well as for constant and linear stress states the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

a fictitious domain method using equilibrated basis functions for harmonic and bi harmonic problems in physics abstract in this paper we present a new meshless method to solve well known problems in physics and engineering with either constant or variable material properties in 2d space harmonic and bi harmonic problems are considered in this paper the method constructs a set of basis functions called equilibrated basis functions eqbfs through a weighted residual integration over a fictitious domain embedding the main one the bases can satisfy the governing partial differential equations approximately chebyshev polynomials of the first kind are employed to construct the eqbfs and exponential functions are used as the weights in the integrals the parameters of the solution are arranged so that all the integrals can be decomposed into much simpler 1d ones over a normalized intervals this reduces the computational efforts significantly either the eqbfs or the results of the integration process may be stored for further use the validity of the results is examined through an extended patch test a set of physical sample problems with variable non variable material properties as the potential flow over a cylinder steady state heat conduction problems in an anisotropic inhomogeneous functionally graded material potential and stokes flow through a channel of finite width obstructed by periodic cylinders and the bending of thin elastic plates having constant or variable thickness are solved to demonstrate the capabilities of the method as a preliminary study we show that the method may effectively be used in a domain decomposition approach

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

enrichment functions for weak singularities in 2d elastic problems with isotropic and orthotropic materials abstract in this paper a new enrichment technique is presented for weak singularities in isotropic and orthotropic 2d linear elasticity problems with absolutely no information of the singularity order in a novel numerical approach the enriching bases are constructed through a weighted residual imposition of the partial differential equation conceptually the bases can be categorized as equilibrated basis functions as another advantage of the proposed technique it will be shown that the enriched solution may be extracted for either isotropic or orthotropic materials in a similar manner noting that singularity effect in orthotropic materials has not been as widely referred to as for isotropic materials in the literature the presented examples selected from the well known literature reveal the accuracy and applicability of the enrichment in the framework of a boundary type method the method may also be found useful for the researchers focusing on the extended finite element method or other similar mesh based or mesh less methods

singular functions for heterogeneous composites with cracks and notches the use of equilibrated singular basis functions abstract in this paper a novel method is presented to solve problems with weak singularities in two dimensional heterogeneous media using equilibrated singular basis functions this especially includes crack problems in composites of functionally graded material types the method is mainly presented in a boundary formulation although it may be found quite useful in other mesh based or mesh less approaches as the extended finite element method xfem the present paper considers harmonic and elasticity problems the most distinguished advantage of the present method is that the solution progress advances without absolutely any knowledge of the analytical singularity order of the problem to this end the partial differential equation of the problem is approximately satisfied in a weighted residual approach after developing the formulation in a mapped polar co ordination some primary basis functions generated from chebyshev polynomials and trigonometric functions along with corresponding weight functions are employed the numerical examples either selected from the well known literature or solved by well established techniques will demonstrate the capability of the method in problems related to composite materials

nonlocal elasticity defined by eringen s integral model introduction of a boundary layer method abstract in this paper we consider a nonlocal elasticity theory defined by eringen s integral model and introduce for the first time a boundary layer method by presenting the exponential basis functions ebfs for such a class of problems the ebfs playing the role of the fundamental solutions are found so that they satisfy the governing equations on an unbounded domain some insight to the theory is given by showing that the ebfs satisfying the navier equations in the classical elasticity theory also satisfy the governing equations in the nonlocal theory some additional ebfs are particularly obtained for the nonlocal theory in order to use the ebfs on bounded domains the effects of the boundary conditions are taken into account by truncating the kernel attenuation function in the constitutive equations this leads to some residuals in the governing equations which appear near the boundaries a weighted residual approach is employed to minimize the residuals near the boundaries the method presented in this paper has much in common with trefftz methods especially when the influence area of the kernel function is much smaller than the main computational domain several one two dimensional problems are solved to demonstrate the way in which the ebfs can be used through the proposed boundary layer method

a boundary collocation meshfree method for the treatment of poisson problems with complex morphologies a new meshfree method based on a discrete transformation of green s basis functions is introduced to simulate poisson problems with complex morphologies the proposed green s discrete transformation method gdtm uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field the optimal number of green s functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition a discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions a comprehensive convergence study is presented to investigate the accuracy and convergence rate of the gdtm we will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit

exponential basis functions in solution of problems with fully incompressible materials in this paper exponential basis functions ebfs satisfying the governing equations of elastic problems with incompressible materials are introduced due to similarity between elasticity problems and steady state fluid problems the bases found for the former problems are used for latter problems we discuss on using single field form known as displacement velocity based formulation and also on using a two field form known as u p formulation in the first formulation we find the pressure bases through performing a limit analysis using a fictitious bulk modulus while in the second formulation the bases are found directly by considering the pressure as a separate variable in the second formulation we directly apply the condition of incompressibility it is shown that both formulations yield identical bases meaning that the first one may be used in a standard approach however it is also shown that when the incompressibility condition is applied by a laplacian of pressure in the second formulation some additional spurious ebfs may be obtained having defined appropriate bases we follow the solution strategy recently introduced by the authors for other engineering problems some well known benchmark problems are solved to show the capabilities of the method

generalization of robustness test procedure for error estimators part ii test results for error estimators using spr and rep in this part of the paper we shall use the formulation given in the first part to assess the quality of recovery based error estimators using two recovery methods i e superconvergent patch recovery spr and recovery by equilibrium in patches rep the recovery methods have been shown to be asymptotically robust and superconvergent when applied to two dimensional problems in this study we shall examine the behaviour of the recovery methods on several three dimensional mesh patterns for patches located either inside or at boundaries this is performed by first finding an asymptotic finite element solution irrespective of boundary conditions at far ends of the domain and then applying the recovery methods the test procedure near kinked boundaries is explained in a step by step manner the results are given in a series of tables and figures for various cases of three dimensional mesh patterns it has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range

inference in linear regression models with many covariates and heteroskedasticity the linear regression model is widely used in empirical work in economics statistics and many other disciplines researchers often include many covariates in their linear model specification in a

exponential basis functions in space and time a meshless method for 2d time dependent problems in this paper we present a method based on using exponential basis functions ebfs to solve well known two dimensional time dependent engineering problems such as elasto dynamic ones the formulation has much in common with those in three dimensional problems while time is taken as the third axis the solution is first approximated by a summation of ebfs and then completed by satisfying the time dependent boundary conditions as well as the initial conditions through a collocation method this is performed by considering a series of spatial and time dependent boundary points to satisfy the boundary conditions through a mixed collocation method the solution method is presented in a time marching form which is capable of solving variety of problems such as transient heat conduction and wave propagation in solids several problems are solved to demonstrate the capabilities of the method

the metrically trimmed mean as a robust estimator of location the metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed a metric the distance from the median is used to determine which points are outlying the influence curve and the asymptotic normality of the metrically trimmed mean are derived using von mises expansions the relative merits of the median the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of nonparametric models with natural parameters it is observed that the metrically trimmed mean works well for the center of symmetry of a symmetric distribution function with asymmetric contamination a multivariate extension of the metrically trimmed mean is discussed

liouville theorems for harmonic maps we prove several liouville theorems for harmonic maps between certain classes of riemannian manifolds in particular the results can be applied to harmonic maps from the euclidean space r m g 0 to a large class of riemannian manifolds our assumptions on the harmonic maps concern the asymptotic behavior of the maps at