higher order properties of the wild bootstrap under misspecification abstract we examine the higher order properties of the wild bootstrap wu 1986 in a linear regression model with stochastic regressors we find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them in the latter case the wild bootstrap may fail to match some of the terms in an edgeworth expansion of the full sample test statistic nonetheless we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation in shrinking neighborhoods of properly specified models to assess the practical implications of this result we conduct a monte carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap

a robust goodness of fit test statistic with application to ordinal regression models we propose a goodness of fit test statistic for linear regression with heterogeneous variance which is asymptotically chi square if the given model is correct the test statistic is computed as a quadratic form of observed minus predicted responses we apply the method to a linear regression for an ordinal categorical response the wheezing status of a child no wheeze wheeze with cold wheeze apart from cold as a function of maternal smoking and city of residence

multiple sign changing solutions to semilinear elliptic resonant problems abstract in this paper we use the topological degree theory and the critical groups to investigate the elliptic equation u f x u in and subject to u 0 on and establish a multiple solutions theorem which guarantees that this problem has at least six nontrivial solutions under some resonant conditions if this problem has only finitely many solutions then of these solutions there are two positive solutions two negative solutions and two sign changing solutions

quasi aitken estimation for heteroskedasticity of unknown form abstract two modifications to standard aitken estimation of heteroskedastic linear regressions are suggested 1 different criteria for calculating unknown parameters to yield more efficient estimates to the coefficients when the form of heteroskedasticity is misspecified and 2 a different way of estimating the covariance matrix of the feasible aitken estimator a sampling experiment provides evidence that the first adjustment could provide more efficient estimates though not clearly more so than alternatives the second adjustment is crucial for reliable inference even when the form of heteroskedasticity is correctly specified

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

a statistical analysis of brain morphology using wild bootstrapping methods for the analysis of brain morphology including voxel based morphology and surface based morphometries have been used to detect associations between brain structure and covariates of interest such as diagnosis severity of disease age iq and genotype the statistical analysis of morphometric measures usually involves two statistical procedures 1 invoking a statistical model at each voxel or point on the surface of the brain or brain subregion followed by mapping test statistics e g t test or their associated p values at each of those voxels 2 correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation we propose the use of new statistical methods for each of these procedures we first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion e g cortical or subcortical surfaces and the covariates of interest moreover we develop a robust test procedure that is based on a resampling method called wild bootstrapping this procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest the value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data including data from both anatomical and functional magnetic resonance imaging fmri simulation studies demonstrate that this robust test procedure can accurately control the family wise error rate we demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects

approximate power functions for some robust tests of regression coefficients approximate power functions for some robust tests of regression coefficients thomas j rothenberg department o f economics u n i v e r s i t y o f c a l i f o r n i a berkeley research papers i n economics no 84 1 summary edgeworth expansions are developed f o r the d i s t r i b u t i o n functions o f some t e s t s t a t i s t i c s i n the normal l i n e a r regression model where the e r r o r covariance matrix i s unknown tests based on generalized l e a s t squares estimates and also on ordinary l e a s t squares estimates are considered in both cases adjustments t o the asymptotic c r i t i c a l the approxi values are found and approximate l o c a l power c a l c u l a t e d and a u t o c o r r e l a t i o n mations are applied to a number o f examples i n c l u d i n g h e t e r o s c e d a s t i c i t y

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

small sample performance of bias corrected sandwich estimators for cluster randomized trials with binary outcomes the sandwich estimator in generalized estimating equations gee approach underestimates the true variance in small samples and consequently results in inflated type i error rates in hypothesis testing this fact limits the application of the gee in cluster randomized trials crts with few clusters under various crt scenarios with correlated binary outcomes we evaluate the small sample properties of the gee wald tests using bias corrected sandwich estimators our results suggest that the gee wald z test should be avoided in the analyses of crts with few clusters even when bias corrected sandwich estimators are used with t distribution approximation the kauermann and carroll kc correction can keep the test size to nominal levels even when the number of clusters is as low as 10 and is robust to the moderate variation of the cluster sizes however in cases with large variations in cluster sizes the fay and graubard fg correction should be used instead furthermore we derive a formula to calculate the power and minimum total number of clusters one needs using the t test and kc correction for the crts with binary outcomes the power levels as predicted by the proposed formula agree well with the empirical powers from the simulations the proposed methods are illustrated using real crt data we conclude that with appropriate control of type i error rates under small sample sizes we recommend the use of gee approach in crts with binary outcomes because of fewer assumptions and robustness to the misspecification of the covariance structure copyright 2014 john wiley sons ltd

the low mach number limit for the full navier stokes fourier system we study the low mach number asymptotic limit for solutions to the full navier stokes fourier system supplemented with ill prepared data and considered on an arbitrary time interval convergencetowards the incompressible navier stokes equations is shown

on systems of cahn hilliard and allen cahn equations considered as gradient flows in hilbert spaces abstract we study systems of allen cahn and cahn hilliard equations with the mobility coefficients depending on c and c we interpret these systems of equations as gradient flows in hilbert spaces with a densely defined riemannian metric in particular we study gradient flows curves of maximal slope of the form t u l u s u f where s is a nonconvex functional l u s u is the strong weak closure of the subgradient of s and f is a time dependent right hand side the article generalizes the results by rossi and savare 36 to this setting and applies for systems of multiple phases derived by heida malek and rajagopal 20 19 in a simplified form more generally we will show that a certain class of reaction diffusion equations coming from a modeling approach by rajagopal and srinivasa 32 or by mielke 27 are automatically subject to the presented theory of curves of maximal slope

bias corrections for two step fixed effects panel data estimators this paper introduces large t bias corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity these models include systems of equations with limited dependent variables and unobserved individual effects and sample selection models with unobserved individual effects our two step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity selection bias we then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable the fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem this problem is exacerbated by the two step nature of the procedure as these two step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large t bias adjustments to an important class of models simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator

multiple solutions for fourth order boundary value problem abstract in this paper we study the existence and multiplicity of nontrivial solutions for the fourth order two point boundary value problems making use of the theory of fixed point index in cone and leray schauder degree under general conditions on nonlinearity we prove that there exist at least six different nontrivial solutions for the fourth order two point boundary value problems furthermore if the nonlinearity is odd we obtain that there exist at least eight different nontrivial solutions

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

existence and multiplicity of solutions to 2mth order ordinary differential equations abstract in this paper the existence and multiplicity of solutions are obtained for the 2mth order ordinary differential equation two point boundary value problems 1 m u 2 m t i 1 m 1 m i a i u 2 m i t f t u t for all t 0 1 subject to dirichlet neumann mixed and periodic boundary value conditions respectively where f is continuous a i r for all i 1 2 m since these four boundary value problems have some common properties and they can be transformed into the integral equation of form u i 1 m a i t i u t m f u we firstly deal with this nonlinear integral equation by using the strongly monotone operator principle and the critical point theory we establish some conditions on f which are able to guarantee that the integral equation has a unique solution at least one nonzero solution and infinitely many solutions furthermore we apply the abstract results on the integral equation to the above four 2mth order two point boundary problems and successfully resolve the existence and multiplicity of their solutions

analyzing two stage experiments in the presence of interference abstracttwo stage randomization is a powerful design for estimating treatment effects in the presence of interference that is when one individual s treatment assignment affects another individual s outcomes our motivating example is a two stage randomized trial evaluating an intervention to reduce student absenteeism in the school district of philadelphia in that experiment households with multiple students were first assigned to treatment or control then in treated households one student was randomly assigned to treatment using this example we highlight key considerations for analyzing two stage experiments in practice our first contribution is to address additional complexities that arise when household sizes vary in this case researchers must decide between assigning equal weight to households or equal weight to individuals we propose unbiased estimators for a broad class of individual and household weighted estimands with corresponding theoretical and estimated variances our second co

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

on thermomechanical restrictions of continua the central idea proposed here is that in entropy producing processes a specific choice from among a competing class of constitutive functions can be made so that the state variables evolve in a way that maximizes the rate of entropy production when attention is restricted to quadratic forms for the rate of entropy production the assumption leads to results that are fully in keeping with linear phenomenological relations that satisfy the onsager relations in other words the usual linear evolution laws such as fourier s law of heat conduction fick s law darcy s law newton s law of viscosity etc all corroborate this assumption we clarify the difference between the maximum rate of entropy production criterion that characterizes choices among constitutive relations and the minimum entropy production theorem due to onsager 1931 that characterizes steady states for special choices of the rate of entropy production we then show that for other forms of entropy production that are not quadratic for which the onsager relations and related theorems cannot be applied we can use the procedure described here to obtain nonlinear laws we demonstrate by means of an example that even yield type phenomena can be accommodated within this framework while they cannot within the framework of onsager we also discuss issues concerning constraints especially in thermoelasticity within the context of our ideas

regression based methods for using control variates in monte carlo experiments abstract methods based on linear regression provide an easy way to use the information in control variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in monte carlo experiments we propose a new technique that allows these methods to be used when the quantities of interest are quantiles we also propose new ways to obtain approximately optimal control variates in many cases of interest these methods seem to work well in practice and can greatly reduce the number of replications required to obtain a given level of accuracy

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

covariance estimators for generalized estimating equations gee in longitudinal analysis with small samples generalized estimating equations gee is a general statistical method to fit marginal models for longitudinal data in biomedical studies the variance covariance matrix of the regression parameter coefficients is usually estimated by a robust sandwich variance estimator which does not perform satisfactorily when the sample size is small to reduce the downward bias and improve the efficiency several modified variance estimators have been proposed for bias correction or efficiency improvement in this paper we provide a comprehensive review on recent developments of modified variance estimators and compare their small sample performance theoretically and numerically through simulation and real data examples in particular wald tests and t tests based on different variance estimators are used for hypothesis testing and the guideline on appropriate sample sizes for each estimator is provided for preserving type i error in general cases based on numerical results moreover we develop a user friendly r package geesmv incorporating all of these variance estimators for public usage in practice

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

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

a numerical scheme for multi point special boundary value problems and application to fluid flow through porous layers abstract in this paper we propose a numerical scheme based on finite differences for the numerical solution of nonlinear multi point boundary value problems over adjacent domains in each subdomain the solution is governed by a different equation the solutions are required to be smooth across the interface nodes the approach is based on using finite difference approximation of the derivatives at the interface nodes smoothness across the interface nodes is imposed to produce an algebraic system of nonlinear equations a modified multi dimensional newton s method is proposed for solving the nonlinear system the accuracy of the proposed scheme is validated by examples whose exact solutions are known the proposed scheme is applied to solve for the velocity profile of fluid flow through multilayer porous media

does modeling a structural break improve forecast accuracy mean square forecast error loss implies a bias variance trade off that suggests that structural breaks of small magnitude should be ignored in this paper we provide a test to determine whether modeling a structural break improves forecast accuracy the test is near optimal even when the date of a local to zero break is not consistently estimable the results extend to forecast combinations that weight the post break sample and the full sample forecasts by our test statistic in a large number of macroeconomic time series we find that structural breaks that are relevant for forecasting occur much less frequently than existing tests indicate

a robust effect size index effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size existing effect size indices are developed for particular parametric models or population parameters here we propose a robust effect size index based on m estimators this approach yields an index that is very generalizable because it is unitless across a wide range of models we demonstrate that the new index is a function of cohen s d formula see text and standardized log odds ratio when each of the parametric models is correctly specified we show that existing effect size estimators are biased when the parametric models are incorrect e g under unknown heteroskedasticity we provide simple formulas to compute power and sample size and use simulations to assess the bias and standard error of the effect size estimator in finite samples because the new index is invariant across models it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences

residual bootstrap tests in linear models with many regressors abstract this paper is concerned with bootstrap hypothesis testing in linear regression models with many regressors i show that bootstrap f l r and l m tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size one of the conditions for these results is that the regressors come from an asymptotically balanced design depending on the number of restrictions tested and on the errors distribution violation of that condition might render the bootstrap tests asymptotically invalid in that case i propose bootstrapping calhoun s 2011 g statistic or modified versions of the l r and l m statistics and show that these procedures remain asymptotically valid monte carlo simulations indicate that the bootstrap tests often outperform asymptotic ones however analyzing the approximate third cumulant of the f statistic reveals that the bootstrap test does not generally provide the usual higher order asymptotic refinements nevertheless it is found that the bootstrap third cumulant partially matches the population third cumulant which might explain the bootstrap s good finite sample performances especially when the errors come from a symmetric distribution

on the power of tests for superexogeneity and structural invariance abstract this paper examines the finite sample power of tests of structural invariance and superexogeneity hypotheses in econometric models with contemporaneous conditioning variables we consider both direct parametric tests of superexogeneity as well as indirect procedures based on temporal stability tests for the parameters of interest our monte carlo analysis reveals that both types of tests may lack power in interesting classes of models an empirical illustration investigates the superexogeneity of the short term interest rate in a dynamic specification for the u s term structure

improved heteroscedasticity consistent covariance matrix estimators summary the heteroscedasticity consistent covariance matrix estimator proposed by white 1980 is commonly used in practical applications and is implemented into a number of pieces of statistical software however although consistent it can display substantial bias in small to moderately large samples as shown by monte carlo simulations elsewhere this paper defines modified white estimators which are approximately bias free numerical results show that the modified estimators display much smaller bias than white s estimator in small samples we also show that the bias correction leads to some variance inflation in hypothesis testing based on heteroscedasticity consistent covariance matrix estimators numerical results suggest that tests based on the proposed bias corrected estimators typically display smaller size distortions

sign changing solutions to second order integral boundary value problems abstract in this paper by using the fixed point index theory and leray schauder degree theory we consider the existence and multiplicity of sign changing solutions to nonlinear second order integral boundary value problem u t f u t for all t 0 1 subject to u 0 0 and u 1 g 0 1 u s d s where f g c r r we obtain some new existence results concerning sign changing solutions by computing hardly eigenvalues and the algebraic multiplicities of the associated linear problem if f and g satisfy certain conditions then this problem has at least six different nontrivial solutions two positive solutions two negative solutions and two sign changing solutions moreover if f and g are also odd then the problem has at least eight different nontrivial solutions which are two positive two negative and four sign changing solutions

maximally dissipative local solutions to rate independent systems and application to damage and delamination problems abstract the system of two inclusions u e t u t z t 0 and r z z e t u t z t 0 with the dissipation potential r degree 1 homogeneous and with the stored energy e t separately convex is considered the relation between conventional weak solutions and local solutions is shown and a suitably integrated maximal dissipation principle is devised to select force driven local solutions and eliminate solutions with too early jumps as it may occur in energy driven ones this is illustrated on scalar examples an approximation by a simple and efficient semi implicit time discretization of the fractional step type is shown to converge to local solutions on the scalar examples the approximate solutions are shown to satisfy the integrated maximal dissipation principle asymptotically while in general it is devised only to serve as an a posteriori tool to justify or possibly adaptively adjust thus obtained approximate solutions as in fact force driven applications of such solutions are illustrated on specific examples from continuum mechanics at small strains involving inelastic processes in a bulk or on a surface namely damage and delamination

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

specification testing in markov switching time series models this paper develops a series of specification tests of markov switching time series models tests for omitted autocorrelation omitted arch misspecification of the markovian dynamics and omitted explanatory variables are proposed all of the tests can be constructed as a natural byproduct of the routine used to calculate the smoothed probability that a given observation came from a particular regime and do not require estimation of additional parameters the paper performs monte carlo analysis of the tests and briefly illustrates their use with an empirical application

a method for smoothing simulated moments of discrete probabilities in multinomial probit models there has been much interest over the years in estimating discrete choice models however with the exception of multinomial logit models agents have been restricted to few choices so that multivariate integrals could be feasibly integrated numerically 2 pakes and pollard 1989 and mcfadden 1989 have independently developed the method of simulated moments msm to deal with estimating a wide class of models of which high order discrete choice models are a subset one of the problems a researcher must handle when using msm for a discrete choice model is how to smooth the discrete simulated random variables this is necessary to keep small the number of draws required to simulate derivatives and to simulate variation in the data geweke 1989 and mcfadden 1989 have suggested importance sampling methods and other methods to smooth the simulated variables for general error structures in this paper i present a factor analytic smoothing method that can be applied to probit problems although it is not as general as the methods geweke and mcfadden suggest it is easy to use and has clear intuition furthermore simulated probabilities will be unbiased will be bounded between zero and unity and will have smaller variances than unsmoothed probabilities always and smaller variances than importance sampling estimates for a large class of probabilities the second section of this paper develops notation defines the problem and presents the smoothing method and an algorithm to employ it the last section presents monte carlo comparisons of the smoothing method to the importance sampling method

on mitigating the analytical limitations of finely stratified experiments although attractive from a theoretical perspective finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block randomized experiments with multiple treated and control individuals in each block in short when using a weighted difference in means to estimate the sample average treatment effect the traditional variance estimator in a paired experiment is conservative unless the pairwise average treatment effects are constant across pairs however in more coarsely stratified experiments the corresponding variance estimator is unbiased if treatment effects are constant within blocks even if they vary across blocks using insights from classical least squares theory we present an improved variance estimator that is appropriate in finely stratified experiments the variance estimator remains conservative in expectation but is asymptotically no more conservative than the classical estimator and can be considerably less conservative the magnitude of the improvement depends on the extent to which effect heterogeneity can be explained by observed covariates aided by this estimator a new test for the null hypothesis of a constant treatment effect is proposed these findings extend to some but not all superpopulation models depending on whether the covariates are viewed as fixed across samples

statistical analysis of diffusion tensors in diffusion weighted magnetic resonance imaging data diffusion tensor imaging has been widely used to reconstruct the structure and orientation of fibers in biological tissues particularly in the white matter of the brain because it can track the effective diffusion of water along those fibers the raw diffusion weighted images from which diffusion tensors are estimated however inherently contain noise noise in the images produces uncertainty in the estimation of the tensors which are 3 3 positive definite matrices and of their derived quantities including eigenvalues eigenvectors and the fiber pathways that are reconstructed based on those tensor elements the aim of this article is to provide a comprehensive theoretical framework of statistical inference for quantifying the effects of noise on diffusion tensors on their eigenvalues and eigenvectors and on their morphological classification we propose a semiparametric model to account for noise in diffusion weighted images we then develop a one step weighted least squares estimate of the t

multiple sign changing solutions to the sturm liouville boundary value problem with resonance abstract in this paper we study the sturm liouville boundary value problem p x u q x u f x u x 0 1 subject to u 0 u 0 u 1 u 1 0 by constructing a new sobolev space h 1 0 1 we discuss the existence of multiple solutions especially the existence of multiple sign changing solutions to this problem when the nonlinear f is resonant both at 0 and by combining the methods of the morse theory the topological degree and the fixed point index we establish a multiple solutions theorem which guarantees that the problem has at least six nontrivial solutions if this problem has only finitely many solutions then of these solutions there are two positive solutions two negative solutions and two sign changing solutions

a class of fourth order singular boundary value problems by constructing lower and upper solutions and with the maximal theorem the author gives a necessary and sufficient condition for the existence of c 2 0 1 as well as c 3 0 1 positive solutions of singular boundary value problems for a class of fourth order sublinear differential equations

resurrecting weighted least squares this paper shows how asymptotically valid inference in regression models based on the weighted least squares wls estimator can be obtained even when the model for reweighting the data is misspecified like the ordinary least squares estimator the wls estimator can be accompanied by heterokedasticty consistent hc standard errors without knowledge of the functional form of conditional heteroskedasticity first we provide rigorous proofs under reasonable assumptions second we provide numerical support in favor of this approach indeed a monte carly study demonstrates attractive finite sample properties compared to the status quo both in terms of estimation and making inference

a covariance estimator for gee with improved small sample properties summary in this paper we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations gee hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small resampling methods such as the jackknife and bootstrap have been suggested for covariance estimation when the number of clusters is small a drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near zero cell counts caused by resampling we propose a bias corrected covariance estimator that avoids this problem in a small simulation study we compare the bias corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10 40 subjects with equal and unequal cluster sizes of 16 64 observations the bias corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2 3 times the nominal level the methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease

solving large classes of nonlinear systems of pdes it is shown that large classes of nonlinear systems of pdes with possibly associated initial and or boundary value problems can be solved by the method of order completion the solutions obtained can be assimilated with hausdorff continuous functions the usual navier stokes equations as well as their various modifications aiming at a realistic modeling are included as particular cases the same holds for the critically important constitutive relations in various branches of continuum mechanics the solution method does not involve functional analysis nor various sobolev or other spaces of distributions or generalized functions the general and type independent existence and regularity results regarding solutions presented here have recently been introduced in the literature provided also if need be that the notion of a solution shall be suitably extended cited from hilbert s 20th problem

moderation analysis using a two level regression model moderation analysis is widely used in social and behavioral research the most commonly used model for moderation analysis is moderated multiple regression mmr in which the explanatory variables of the regression model include product terms and the model is typically estimated by least squares ls this paper argues for a two level regression model in which the regression coefficients of a criterion variable on predictors are further regressed on moderator variables an algorithm for estimating the parameters of the two level model by normal distribution based maximum likelihood nml is developed formulas for the standard errors ses of the parameter estimates are provided and studied results indicate that when heteroscedasticity exists nml with the two level model gives more efficient and more accurate parameter estimates than the ls analysis of the mmr model when error variances are homoscedastic nml with the two level model leads to essentially the same results as ls with the mmr model most importantly the two level regression model permits estimating the percentage of variance of each regression coefficient that is due to moderator variables when applied to data from general social surveys 1991 nml with the two level model identified a significant moderation effect of race on the regression of job prestige on years of education while ls with the mmr model did not an r package is also developed and documented to facilitate the application of the two level model

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

multiple solutions of some boundary value problems with parameters abstract in this paper we study the existence and multiplicity of nontrivial solutions for the following second order dirichlet nonlinear boundary value problem with odd order derivative u t a u t b u t f t u t for all t 0 1 with u 0 u 1 0 where a b r 1 f c 1 0 1 r 1 r 1 by using the morse theory we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution two nontrivial solutions and infinitely many solutions separately

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

empirically relevant critical values for hypothesis tests a bootstrap approach tests of statistical hypotheses can be based on either of two critical values the type i critical value or the size corrected critical value the former usually depends on unknown population parameters and cannot be evaluated exactly in applications but it can often be estimated very accurately by using the bootstrap the latter does not depend on unknown population parameters but is likely to yield a test with low power the critical values used in most monte carlo studies of the powers of tests are neither type i nor size corrected they are irrelevant to empirical research

a random effects model for ordered categorical data abstract this article presents a random effects model for multivariate and grouped univariate ordered categorical data the assumed family of distributions for the random effects adopts a wide variety of forms and shapes the model s likelihood has a closed expression and can be computed without recourse to numerical integration or gaussian quadrature a bivariate and a grouped univariate example are used to illustrate the proposed model

simulation based finite sample tests for heteroskedasticity and arch effects tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations we show that the size of such tests can be perfectly controlledin nite samples through monte carlo test techniques with both gaussian and non gaussian heavy tailed disturbance distributions the procedures studied include standard heteroskedasticity tests e g glejser bartlett cochran hartley breusch pagan godfrey white szroeter as well as tests for arch type heterosked asticity sup type andcombinedtests are also proposedto allow for unknown breakpoints in the variance the fact that the proposedproced ures achieve size control andhave goodpower is demonstrated in a monte carlo simulation c 2003 elsevier b v all rights reserved

generalization of the dynamical lack of fit reduction from generic to generic the lack of fit statistical reduction developed and formulated first by bruce turkington is a general method taking liouville equation for probability density detailed level and transforming it to reduced dynamics of projected quantities less detailed level in this paper the method is generalized the hamiltonian liouville equation is replaced by an arbitrary hamiltonian evolution combined with gradient dynamics generic the boltzmann entropy is replaced by an arbitrary entropy and the kinetic energy by an arbitrary energy the gradient part is a generalized gradient dynamics generated by a dissipation potential the reduced evolution of the projected state variables is shown to preserve the generic structure of the original detailed level evolution the dissipation potential is obtained by solving a hamilton jacobi equation in summary the lack of fit reduction can start with generic and obtain generic for the reduced state variables

heteroscedasticity robust inference in linear regression models with many covariates we consider inference in linear regression models that is robust to heteroscedasticity and the presence of many control variables when the number of control variables increases at the same rate as

the finite sample distributions of heteroskedasticity robust wald statistics the imhof procedure is used to calculate the exact finite sample distributions of alternative heteroskedasticity robust wald type tests of scalar linear hypothesis in the normal linear model the tests are distinguished by the variance estimator that they use these include the white eicker and jackknife estimators the calculations demonstrate the importance of regression design in determining the quality of conventional first order asymptotic approximations to the null distributions of the tests

some improvements in confidence intervals for standardized regression coefficients yuan and chan psychometrika 76 670 690 2011 doi 10 1007 s11336 011 9224 6 derived consistent confidence intervals for standardized regression coefficients under fixed and random score assumptions jones and waller psychometrika 80 365 378 2015 doi 10 1007 s11336 013 9380 y extended these developments to circumstances where data are non normal by examining confidence intervals based on browne s br j math stat psychol 37 62 83 1984 doi 10 1111 j 2044 8317 1984 tb00789 x asymptotic distribution free adf theory seven different heteroscedastic consistent hc estimators were investigated in the current study as potentially better solutions for constructing confidence intervals on standardized regression coefficients under non normality normal theory adf and hc estimators were evaluated in a monte carlo simulation findings confirmed the superiority of the hc3 mackinnon and white j econ 35 305 325 1985 doi 10 1016 0304 4076 85 90158 7 and hc5 cribari neto and da silva adv stat anal 95 129 146 2011 doi 10 1007 s10182 010 0141 2 interval estimators over jones and waller s adf estimator under all conditions investigated as well as over the normal theory method the hc5 estimator was more robust in a restricted set of conditions over the hc3 estimator some possible extensions of hc estimators to other effect size measures are considered for future developments

asymptotic theory and wild bootstrap inference with clustered errors abstract we study inference based on cluster robust variance estimators for regression models with clustered errors focusing on the wild cluster bootstrap we state conditions under which asymptotic and bootstrap tests and confidence intervals are asymptotically valid these conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity we also derive edgeworth expansions for the asymptotic and bootstrap test statistics simulation experiments illustrate the theoretical results and suggest that alternative variants of the wild cluster bootstrap may perform quite differently the edgeworth expansions explain the overrejection of asymptotic tests and shed light on the choice of auxiliary distribution and whether to use restricted or unrestricted estimates in the bootstrap data generating process

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

comparison of bootstrap approaches for estimation of uncertainties of dti parameters bootstrap is an empirical non parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor mri dti parameters useful in tractography and in assessing dti methods the current bootstrap method repetition bootstrap used for dti analysis performs resampling within the data sharing common diffusion gradients requiring multiple acquisitions for each diffusion gradient recently wild bootstrap was proposed that can be applied without multiple acquisitions in this paper two new approaches are introduced called residual bootstrap and repetition bootknife we show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and therefore better estimates the standard errors like wild bootstrap residual bootstrap is applicable to single acquisition scheme and both are based on regression residuals called model based resampling residual bootstrap is based on the assumption that non constant variance of measured diffusion attenuated signals can be modeled which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor the performances of these bootstrap approaches were compared in terms of bias variance and overall error of bootstrap estimated standard error by monte carlo simulation we demonstrate that residual bootstrap has smaller biases and overall errors which enables estimation of uncertainties with higher accuracy understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on dti parameters probabilistic fiber tracking and optimizing dti methods

the method of lower and upper solutions for a bending of an elastic beam equation abstract in this paper by combining a new maximum principle and the theory of the two parameter linear eigenvalue problem we develop the monotone method in the presence of lower and upper solutions for the problem u 4 x f x u x u x 0 x 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

an optimized wild bootstrap method for evaluation of measurement uncertainties of dti derived parameters in human brain evaluation of measurement uncertainties or errors in diffusion tensor derived parameters is essential to quantify the sensitivity and specificity of these quantities as potential surrogate biomarkers for pathophysiological processes with diffusion tensor imaging dti computational methods such as the monte carlo simulation have provided insights into characterization of the measurement uncertainty in dti however due to the complexity of real brain data as well as different sources of variations during the image acquisition a robust estimator for dti measurement uncertainty in human brain is required recent studies have shown that wild bootstrap a novel nonparametric statistical method can potentially provide effective estimations of dti measurement uncertainties in human brain dti data in this study we further optimized the dti application of the wild bootstrap method for typical clinical applications we evaluated the validity of wild bootstrap utilizing numerical simulations with different combinations of dti protocol parameters and wild bootstrap experimental designs and quantitatively compared estimates of uncertainties from wild bootstrapping with those from monte carlo simulations our results demonstrate that a wild bootstrap implementation using at least 1000 wild bootstrap iterations with a type ii or type iii heteroskedasticity consistent covariance matrix estimator provides robust evaluations of most dti protocols

a gibbs potential based formulation for obtaining the response functions for a class of viscoelastic materials in this article we demonstrate the use of a gibbs potential based formulation as a means for developing a thermodynamically consistent model for a class of viscoelastic fluids of the rate type since one cannot always use a formulation based on a helmholtz potential to model rate type models the formulation takes on added significance the salient features of this approach are the following this approach provides a thermodynamical rationalization of many commonly used models that are developed on purely phenomenological grounds furthermore the study provides a framework for generating other classes of models and allows for a relatively straightforward means for the inclusion of thermal effects the approach provides a simple means for including anisotropic effects without the need for directors or other new internal variables and the approach does not use any additional variables such as conformation tensors or elastic strains measured from stress free configurations other than the current or cauchy stress the current mass density and the velocity gradient we also show how the entire structure of the theory is obtained from just two scalar functions the gibbs potential and the rate of dissipation function

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

positive solutions of some nonlocal fourth order boundary value problem by the use of the krasnosel skii s fixed point theorem the existence of one or two positive solutions for the nonlocal fourth order boundary value problemu 4 t email protected t email protected t u t u t 00 email protected c 0 1 x 0 x 0 0

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

the wild bootstrap tamed at last the wild bootstrap is studied in the context of regression models with heteroskedastic disturbances we show that in one very specific case perfect bootstrap inference is possible and a substantial reduction in the error in the rejection probability of a bootstrap test is available much more generally however the version of the wild bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild bootstrap simulation experiments show that this does not prevent the preferred version from having the smallest error in rejection probability in small and medium sized samples

fixed effects estimation of structural parameters and marginal effects in panel probit models fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem in this paper i characterize the leading term of a large t expansion of the bias of the mle and estimators of average marginal effects in parametric fixed effects panel binary choice models for probit index coefficients the former term is proportional to the true value of the coefficients being estimated this result allows me to derive a lower bound for the bias of the mle i then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity i subsequently propose new bias corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors

positive solutions of fourth order two point boundary value problems in this paper by using the krasnoselskii fixed point theorem we study the existence of one or multiple positive solution of the fourth order two point boundary value problem y 4 t f t y t y t y 0 y 1 y 0 y 1 0 we also give some examples to illustrate our results

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

two step estimation of heteroskedastic sample selection models abstract this paper considers two step estimation of a sample selection model in which there is heteroskedasticity of unknown form in the latent errors we propose an estimator which uses recent developments in nonparametric regression estimation involving series approximations the estimator is shown to be consistent and asymptotically normally distributed under reasonable conditions a small monte carlo experiment demonstrates the usefulness of the estimator and highlights the bias inherent in the usual heckman 1979 estimator when there is heteroskedasticity

marginal analysis of ordinal clustered longitudinal data with informative cluster size the issue of informative cluster size ics often arises in the analysis of dental data ics describes a situation where the outcome of interest is related to cluster size much of the work on modeling marginal inference in longitudinal studies with potential ics has focused on continuous outcomes however periodontal disease outcomes including clinical attachment loss are often assessed using ordinal scoring systems in addition participants may lose teeth over the course of the study due to advancing disease status here we develop longitudinal cluster weighted generalized estimating equations cwgee to model the association of ordinal clustered longitudinal outcomes with participant level health related covariates including metabolic syndrome and smoking status and potentially decreasing cluster size due to tooth loss by fitting a proportional odds logistic regression model the within teeth correlation coefficient over time is estimated using the two stage quasi least squares method the motivation for our work stems from the department of veterans affairs dental longitudinal study in which participants regularly received general and oral health examinations in an extensive simulation study we compare results obtained from cwgee with various working correlation structures to those obtained from conventional gee which does not account for ics our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach