empirical correction to the likelihood ratio statistic for structural equation modeling with many variables survey data typically contain many variables structural equation modeling sem is commonly used in analyzing such data the most widely used statistic for evaluating the adequacy of a sem model is t ml a slight modification to the likelihood ratio statistic under normality assumption t ml approximately follows a chi square distribution when the number of observations n is large and the number of items or variables p is small however in practice p can be rather large while n is always limited due to not having enough participants even with a relatively large n empirical results show that t ml rejects the correct model too often when p is not too small various corrections to t ml have been proposed but they are mostly heuristic following the principle of the bartlett correction this paper proposes an empirical approach to correct t ml so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi square distribution results show that empirically corrected statistics follow the nominal chi square distribution much more closely than previously proposed corrections to t ml and they control type i errors reasonably well whenever n max 50 2p the formulations of the empirically corrected statistics are further used to predict type i errors of t ml as reported in the literature and they perform well

sharp l 2 error estimates and superconvergence of mixed finite element methods for non fickian flows in porous media a sharper l2 error estimate is obtained for the non fickian flow of fluid in porous media by means of a mixed ritz volterra projection instead of the mixed ritz projection used in r e ewing y lin and j wang acta math univ comenian n s 70 2001 pp 75 84 moreover local l2 superconvergence for the velocity along the gauss lines and for the pressure at the gauss points is derived for the mixed finite element method via the ritz volterra projection and global l2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique on the basis of the superconvergence estimates some useful a posteriori error estimators are presented for this mixed finite element method

superconvergence of fully discrete rectangular mixed finite element methods of parabolic control problems in this paper we investigate the superconvergence property of the numerical solution of a quadratic parabolic optimal control problem by using fully discrete mixed finite element methods the space discretization of the state variable is done using usual mixed finite elements whereas the time discretization is based on difference methods the state and the co state are approximated by the lowest order raviart thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions we derive the superconvergence results for the control and the state approximation some numerical examples are presented to confirm the theoretical investigations

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

likelihood ratio testing for admixture models with application to genetic linkage analysis we consider likelihood ratio tests lrt and their modifications for homogeneity in admixture models the admixture model is a two component mixture model where one component is indexed by an unknown parameter while the parameter value for the other component is known this model is widely used in genetic linkage analysis under heterogeneity in which the kernel distribution is binomial for such models it is long recognized that testing for homogeneity is nonstandard and the lrt statistic does not converge to a conventional 2 distribution in this article we investigate the asymptotic behavior of the lrt for general admixture models and show that its limiting distribution is equivalent to the supremum of a squared gaussian process we also discuss the connection and comparison between lrt and alternative approaches such as modifications of lrt and score tests including the modified lrt fu chen and kalbfleisch 2006 statistica sinica 16 805 823 the lrt is an omnibus test that is powerful to detect general alternative hypotheses in contrast alternative approaches may be slightly more powerful to detect certain type of alternatives but much less powerful for others our results are illustrated by simulation studies and an application to a genetic linkage study of schizophrenia

bootstrap inference for instrumental variable models with many weak instruments this study s main contribution is to theoretically analyze the application of bootstrap methods to instrumental variable models when the available instruments may be weak and the number of instruments goes to infinity with the sample size we demonstrate that a standard residual based bootstrap procedure cannot consistently estimate the distribution of the limited information maximum likelihood estimator or fuller 1977 estimator under many many weak instrument sequence the primary reason is that the standard procedure fails to capture the instrument strength in the sample adequately in addition we consider the restricted efficient re bootstrap of davidson and mackinnon 2008 2010 2014 that generates bootstrap data under the null restricted and uses an efficient estimator of the coefficient of the reduced form equation efficient we find that the re bootstrap is also invalid however it effectively mimics more key features in the limiting distributions of interest and thus is less distorted in finite samples than the standard bootstrap procedure finally we propose modified bootstrap procedures that provide a valid distributional approximation for the two estimators with many many weak instruments a monte carlo experiment shows that hypothesis testing based on the asymptotic normal approximation can have severe size distortions in finite samples instead our modified bootstrap procedures greatly reduce these distortions

bootstrap confidence bands for shrinkage estimators empirical application of shrinkage estimators has been limited by the inability to estimate confidence intervals we investigate confidence band estimators based on edgeworth expansions and bootstrapping our monte carlo results suggest that both efron s bias correction method with acceleration and the simple percentile bootstrap methods generate reasonable confidence bands approximations based on edgeworth expansions performed poorly we then use the percentile method with a single bootstrap to generate bands for predictions of gnp growth rates from a leading indicators model our study shows that simple percentile bootstrap confidence bands perform well enough to support empirical applications of shrinkage estimators

bootstrap critical values for tests based on the smoothed maximum score estimator the smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions however the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first order asymptotics are used to obtain critical values this paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values a set of monte carlo experiments illustrates the numerical performance of the bootstrap

robust confidence intervals for average treatment effects under limited overlap limited overlap between the covariate distributions of groups with different treatment assignments does not only make estimates of average treatment effects rather imprecise but can also lead to substantially distorted confidence intervals this paper argues that this is because the coverage error of traditional confidence intervals is driven by the number of observations in the areas of limited overlap some of these local sample sizes can be very small in applications up to the point that distributional approximations derived from classical asymptotic theory become unreliable building on this observation this paper constructs confidence intervals based on classical approaches to small sample inference the approach is easy to implement and has superior theoretical and practical properties relative to standard methods in empirically relevant settings

convergence of finite element approximations to state constrained convex parabolic boundary control problems this paper is concerned with the numerical solution of state constrained parabolic boundary control problems by finite element approximations error estimates for the optimal values and in the coercive case for the optimal solutions are derived these estimates are used to prove convergence results under rather weak assumptions in the noncoercive case a bang bang principle is shown to obtain convergence results for the discrete controls also a discussion of several numerical examples concludes the paper

hypothesis testing under mixture models application to genetic linkage analysis summary in this paper we propose a new class of statistics to test a simple hypothesis against a family of alternatives characterized by a mixture model unlike the likelihood ratio statistic whose large sample distribution is still unknown in this situation these new statistics have a simple asymptotic distribution to which to refer under the null hypothesis simulation results suggest that it has adequate power in detecting the alternatives its application to genetic linkage analysis in the presence of the genetic heterogeneity that motivated this work is emphasized

semiparametric estimation of a work trip mode choice model abstract a binary response model of choice between automobile and transit for travel to work is estimated using fixed and random coefficients probit specifications a semiparametric single index specification and a semiparametric specification that permits arbitrary heteroskedasticity of unknown form the estimation methods are maximum likelihood for the probit models semiparametric quasi maximum likelihood for the single index model and maximum score and smoothed maximum score for the arbitrarily heteroskedastic model specification tests result in rejection of the fixed coefficients probit and single index models but not of the random coefficients probit model and the semiparametric model with arbitrary heteroskedasticity

double bootstrap for shrinkage estimators computer intensive bootstrap methods are potentially problematic when applied to biased estimators similar to ridge regression because biased estimators may lack a pivot we propose a modification for efron s bias corrected percentiles and suggest an approximate pivoting transformation for ridge regression we indicate practical aspects of beran s double bootstrap designed specifically for situations where there is nonnormality and a lack of a pivot econometric applications to estimating consumption functions a simulation with multicollinear data and new graphical tools are included

a fast score test for generalized mixture models in biomedical studies testing for homogeneity between two groups where one group is modeled by mixture models is often of great interest this paper considers the semiparametric exponential family mixture model proposed by hong et al 2017 and studies the score test for homogeneity under this model the score test is nonregular in the sense that nuisance parameters disappear under the null hypothesis to address this difficulty we propose a modification of the score test so that the resulting test enjoys the wilks phenomenon in finite samples we show that with fixed nuisance parameters the score test is locally most powerful in large samples we establish the asymptotic power functions under two types of local alternative hypotheses our simulation studies illustrate that the proposed score test is powerful and computationally fast we apply the proposed score test to an uk ovarian cancer dna methylation data for identification of differentially methylated cpg sites

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

finite element approximation of parabolic time optimal control problems the numerical approximation of a parabolic time optimal control problem via piecewise linear splines is considered at each stage of the approximation a bang bang approximate control is selected by solving for its switching times as the solution of a constrained nonlinear least squares optimization problem the well posedness of the approximation scheme is shown and the rate of convergence to the exact solution investigated numerical results for some one and two dimensional parabolic control problems are given

adaptive finite element methods for optimal control of partial differential equations basic concept a new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations the lagrangian formalism yields the first order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive galerkin finite element method the mesh design in the resulting reduced models is controlled by residual based a posteriori error estimates these are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error in this case the computed state and costate variables can be used as sensitivity factors multiplying the local cell residuals in the error estimators this results in a generic and simple algorithm for mesh adaptation within the optimization process this method is developed and tested for simple boundary control problems in semiconductor models

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

estimation and inference for the causal effect of receiving treatment on a multinomial outcome this article considers the analysis of two arm randomized trials with noncompliance which have a multinomial outcome we first define the causal effect in these trials as some function of outcome distributions of compliers with and without treatment e g the complier average causal effect the measure of stochastic superiority of treatment over control for compliers then estimate the causal effect with the likelihood method next based on the likelihood ratio lr statistic we test those functions of or the equality of the outcome distributions of compliers with and without treatment although the corresponding lr statistic follows a chi squared chi 2 distribution asymptotically when the true values of parameters are in the interior of the parameter space under the null its asymptotic distribution is not chi 2 when the true values of parameters are on the boundary of the parameter space under the null therefore we propose a bootstrap double bootstrap version of a lr test for the causal effect in these trials the methods are illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices

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

bootstrapping improved estimators for linear regression models abstract since stein 1955 proved that the least squares ls estimator for the linear regression model is inadmissible and james and stein 1961 demonstrated a superior estimator under squared error loss a number of better estimators have been proposed one reason these estimators have not been used in empirical work is that it is difficult to derive their sampling distributions this study shows that nonparametric bootstrapping provides good estimates of the sampling distribution of mundlak s 1981 restricted principal components estimator and a new stein rule estimator which shrinks mundlak s towards ls a monte carlo study of the bootstrap is performed for a range of increasingly collinear designs with 100 observations and 10 regressors using a squared error loss function the stein rule estimator performed much better than ls over most of the designs the nonparametric bootstrap generated reasonable estimates of the estimator s risk as well as standard errors of the individual components

statistical testing of genetic linkage under heterogeneity summary recent advances in human genetics have led to a renewed interest in statistical methods for the detection of linkage from family data for example between marker loci and disease traits statistical analysis of linkage between two loci is carried out almost exclusively by means of the lod log odds score test equivalent to a likelihood ratio test the current practice is to declare genetic linkage between loci when the maximum lod score exceeds 3 as will be discussed here the lod score approach is not appropriate for the detection of linkage from heterogeneous data e g when families consist of a mixture of linked and unlinked types heterogeneity may arise for example when rare mutations at different genetic loci are responsible for the same disease trait as an alternative approach to account for possible heterogeneity in the detection of linkage we propose the application of largesample test statistics that are members of neyman s class of c av or partial score tests the convergence of the proposed test statistics to their asymptotic distributions is investigated via monte carlo simulation for typical study designs applicable in human genetics

accurate bootstrap confidence limits for the cumulative hazard and survivor functions under random censoring abstract in clinical trials and other settings confidence intervals for survival probabilities at a fixed point in time are often required typically such intervals are constructed on the cumulative hazard scale the quantiles required for computing these intervals are generally obtained using a first order normal theory approximation the appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect we demonstrate that significant improvement is possible for randomly censored data using the nonparametric bootstrap in particular using edgeworth expansion it is shown that the percentile t and bc a bootstrap methodologies based on the studentized nelson aalen estimator yield second order correct confidence limits for the cumulative hazard function at a fixed time point an explicit formula for the correction term of the edgeworth expansion is found easy to compute estimators for the components of the correction term are also found and lead to simple analytic

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

a priori error estimates for space time finite element discretization of parabolic optimal control problems part i problems without control constraints in this paper we develop a priori error analysis for galerkin finite element discretizations of optimal control problems governed by linear parabolic equations the space discretization of the state variable is done using usual conforming finite elements whereas the time discretization is based on discontinuous galerkin methods for different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters the paper is divided into two parts in the first part we develop some stability and error estimates for space time discretization of the state equation and provide error estimates for optimal control problems without control constraints in the second part of the paper the techniques and results of the first part are used to develop a priori error analysis for optimal control problems with pointwise inequality constraints on the control variable

confidence regions for evolutionary trajectories we derive confidence regions for the evolutionary trajectories derived from a model of via and lande 1985 evolution 39 505 522 we utilize a nested parametric bootstrap to calculate the confidence regions and show that a likelihood based approach provides an unsatisfactory solution we calculate the predicted evolutionary trajectories and confidence regions using data from an experiment on pupal weight of tribolium beetles in two different flour types with realistic sample sizes for experiments that estimate genetic parameters in multiple environments the confidence regions are likely to be large potentially limiting the ability to test hypotheses about evolutionary trajectories the problem may be less acute for trajectories of characters expressed in only a single environment because sample sizes can generally be larger than in multienvironmental studies

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

a posteriori error estimates for optimal control problems governed by parabolic equations in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation we obtain a posteriori error estimates for both the state and the control approximation such estimates which are apparently not available in the literature are an important step towards developing reliable adaptive finite element approximation schemes for the control problem

evaluation of a three step method for choosing the number of bootstrap repetitions abstract this paper provides a variety of monte carlo simulations that evaluate the finite sample performance of the three step method for choosing the number of bootstrap repetitions suggested by andrews and buchinsky econometrica 67 2000 23 51 the simulations cover bootstrap standard errors confidence intervals tests and p values three commonly used econometric applications are considered linear regression binary probit and quantile regression in brief we find that the three step method works very well in all of the contexts examined here we also find that the number of bootstrap repetitions commonly used in econometric applications is much less than needed to achieve accurate bootstrap quantities

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

asymptotic refinements of a misspecification robust bootstrap for gel estimators abstract i propose a nonparametric iid bootstrap procedure for the empirical likelihood the exponential tilting and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals and wald tests and confidence regions based on such estimators furthermore the proposed bootstrap is robust to model misspecification i e it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not this result is new because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification monte carlo experiments are conducted in dynamic panel data setting to support the theoretical finding as an application bootstrap confidence intervals for the returns to schooling of hellerstein and imbens 1999 are calculated the result suggests that the returns to schooling may be higher

high order approximations and generalized necessary conditions for optimality in this paper we derive generalized necessary conditions for optimality for an optimization problem with equality and inequality constraints in a banach space the equality constraints are given in operator form as q x in x f x 0 where f x rightarrow y is an operator between banach spaces the inequality constraints are given by smooth functionals or by closed convex sets models of this type are common in the optimal control problem the paper addresses the case when the frechet derivative f x is not onto and hence the classical lyusternik theorem does not apply to describe the tangent space to q in this case the classical euler lagrange type necessary conditions are trivially satisfied generating abnormal cases a high order generalization of the lyusternik theorem derived earlier u ledzewicz and h schattler nonlinear anal 34 1998 pp 793 815 is used to calculate high order tangent cones to the equality constraint at points x in q where f x is not onto combining these with high order approximating cones related to the other constraints of the problem feasible cones respectively cones of decrease a high order generalization of the dubovitskii milyutin theorem is given and then applied to derive generalized necessary conditions for optimality these conditions reduce to classical conditions for normal cases but they give new and nontrivial conditions for abnormal cases

a model of fractional cointegration and tests for cointegration using the bootstrap abstract the paper proposes a framework for modelling cointegration in fractionally integrated processes and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap in these procedures arfima models are fitted to the data and the estimates used to simulate the null hypothesis of non cointegration in a vector autoregressive modelling framework the simulations are used to estimate p values for alternative regression based test statistics including the f goodness of fit statistic the durbin watson statistic and estimates of the residual d the bootstrap distributions are economical to compute being conditioned on the actual sample values of all but the dependent variable in the regression the procedures are easily adapted to test stronger null hypotheses such as statistical independence the tests are not in general asymptotically pivotal but implemented by the bootstrap are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals as an example the tests are applied to the series for uk consumption and disposable income the power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data the f test performs better in these experiments than the residual based tests although the durbin watson in turn dominates the test based on the residual d

superconvergence of mixed finite element approximations over quadrilaterals a superconvergence result is established in this article for approximate solutions of second order elliptic equations by mixed finite element methods over quadrilaterals the superconvergence indicates an accuracy of cal o h k 2 for the mixed finite element approximation if the raviart thomas or brezzi douglas fortin marini elements of order k are employed with optimal error estimate of cal o h k 1 numerical experiments are presented to illustrate the theoretical result

a three step method for choosing the number of bootstrap repetitions this paper considers the problem of choosing the number of bootstrap repetitions b for bootstrap standard errors confidence intervals confidence regions hypothesis tests p values and bias correction for each of these problems the paper provides a three step method for choosing b to achieve a desired level of accuracy accuracy is measured by the percentage deviation of the bootstrap standard error estimate confidence interval length test s critical value test s p value or bias corrected estimate based on b bootstrap simulations from the corresponding ideal bootstrap quantities for which b the results apply quite generally to parametric semiparametric and nonparametric models with independent and dependent data the results apply to the standard nonparametric iid bootstrap moving block bootstraps for time series data parametric and semiparametric bootstraps and bootstraps for regression models based on bootstrapping residuals monte carlo simulations show that the proposed methods work very well

likelihood ratio testing in linear state space models an application to dynamic stochastic general equilibrium models abstract this paper considers the problem of hypothesis testing in linear gaussian state space models we consider two hypotheses of interest a simple null and a hypothesis of explicit parameter restrictions we derive the asymptotic distributions of the corresponding likelihood ratio test statistics and compute the bartlett adjustments the results are non trivial because the unrestricted state space model is not even locally identified we apply our analysis to test the validity of the dynamic stochastic general equilibrium dsge models a monte carlo exercise illustrates our findings and confirms the importance of bartlett corrections at sample sizes typically encountered in macroeconomics

prepivoting to reduce level error of confidence sets summary approximate confidence sets for a parameter 0 may be obtained by referring a function of 0 and of the sample to an estimated quantile of that function s sampling distribution we call this function the root of the confidence set either asymptotic theory or bootstrap methods can be used to estimate the desired quantile when the root is not a pivot in the sense of classical statistics the actual level of the approximate confidence set may differ substantially from the intended level prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function prepivoting can be iterated bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root the first prepivoting is nearly equivalent to studentizing when that operation is appropriate further iterations of prepivoting make higher order corrections automatically

superconvergence of mixed finite element methods for optimal control problems t in this paper we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods the state and co state variables are approximated by the lowest order raviart thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions some realistic regularity assumptions are presented and applied to error estimation by using an operator interpolation technique we derive l 2 superconvergence properties for the flux functions along the gauss lines and for the scalar functions at the gauss points via mixed projections moreover global l 2 superconvergence results are obtained by virtue of an interpolation postprocessing technique thus based on these superconvergence estimates some asymptotic exactness a posteriori error estimators are presented for the mixed finite element methods finally some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence

the power of bootstrap and asymptotic tests the bootstrap discrepancy measures the difference in rejection probabilities between a bootstrap test and one based on the true distribution the order of magnitude of the bootstrap discrepancy is the same under the null hypothesis and under non null processes described by pitman drift if the test statistic is not an exact pivot critical values depend on which data generating process dgp is used to determine the null distribution we propose using the dgp which minimizes the bootstrap discrepancy we also show that under an asymptotic independence condition the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation

asymptotic distribution of p values in composite null models abstract we investigate the compatibility of a null model h 0 with the data by calculating a p value that is the probability under h 0 that a given test statistic t exceeds its observed value when the null model consists of a single distribution the p value is readily obtained and it has a uniform distribution under h 0 on the other hand when the null model depends on an unknown nuisance parameter one must somehow get rid of e g by estimating it to calculate a p value various proposals have been suggested to remove each yielding a different candidate p value but unlike the simple case these p values typically are not uniformly distributed under the null model in this article we investigate their asymptotic distribution under h 0 we show that when the asymptotic mean of the test statistic t depends on the posterior predictive p value of guttman and rubin and the plug in p value are conservative i e their asymptotic distributions are more concentrated around 1 2 than a uni

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

using bootstrap likelihood ratios in finite mixture models statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non regular problem the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a non identifiable subset of the parameter space the maximum likelihood estimator is shown to converge to the subset characterized by the same density function and connection is made to the bootstrap method proposed by aitkin and co workers and mclachlan for testing the number of components in a finite mixture and deriving confidence regions in a finite mixture

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

double bootstrap methods that use a single double bootstrap simulation we show that when the double bootstrap is used to improve performance of bootstrap methods for bias correction techniques based on using a single double bootstrap sample for each single bootstrap sample can be particularly effective in particular they produce third order accuracy for much less computational expense than is required by conventional double bootstrap methods however this improved level of performance is not available for the single double bootstrap methods that have been suggested to construct confidence intervals or distribution estimators

asymptotic refinements of a misspecification robust bootstrap for generalized method of moments estimators i propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on gmm estimators even when the model is misspecified in addition my bootstrap does not require recentering the moment function which has been considered as critical for gmm regardless of model misspecification the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification the key idea is to link the misspecified bootstrap moment condition to the large sample theory of gmm under misspecification of hall and inoue 2003 two examples are provided combining data sets and invalid instrumental variables

superconvergence of quadratic optimal control problems by triangular mixed finite element methods the aim of this work is to investigate the discretization of a quadratic convex optimal control problem using the mixed finite element method the state and co state are approximated by the order k 1 raviart thomas mixed finite element spaces and the control is approximated by piecewise constant functions we construct an interpolation of the exact control and a projection of the discrete scalar co state to be the approximated solution of the control variable for the continuous optimal control problem as a result it can be proved that the difference between the interpolation and the piecewise constant approximation has superconvergence property for the control of order h 3 2 for k 0 and of order h 2 for k 1 moreover only for the order k 1 raviart thomas mixed finite element approximation does the postprocessing technique possess the superconvergence property of order h 2 finally some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence

simulated power functions on etudie par simulation la puissance de huit tests contre des alternatives comportant le meme parametre de puissance inconnu

a new method for testing separate families of hypotheses abstract theoretical and empirical evidence are reported showing that the tests given in cox 1961 and williams 1970a b for the problem of testing separate families of hypotheses suffer from fundamental difficulties neither test is guaranteed to be asymptotically level a even for very smooth problems a new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions theoretical properties of the method are derived and its finite sample behavior is studied in a number of examples

the ios test for model misspecification a new test of model misspecification is proposed based on the ratio of in sample and out of sample likelihoods the test is broadly applicable and in simple problems approximates well known intuitive methods using jackknife influence curve approximations it is shown that the test statistic can be viewed asymptotically as a multiplicative contrast between two estimates of the information matrix both of which are consistent under correct model specification this approximation is used to show that the statistic is asymptotically normally distributed although it is suggested that p values be computed using the parametric bootstrap the resulting methodology is demonstrated with various examples and simulations involving both discrete and continuous data

plmet a novel pseudolikelihood based em test for homogeneity in generalilzed exponential tilt mixture models motivated by analyses of dna methylation data we propose a semiparametric mixture model namely the generalized exponential tilt mixture model to account for heterogeneity between differentially methylated and non differentially methylated subjects in the cancer group and capture the differences in higher order moments e g mean and variance between subjects in cancer and normal groups a pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function to circumvent boundary and non identifiability problems as in parametric mixture models we modify the pseudolikelihood by adding a penalty function in addition the test with simple asymptotic distribution has computational advantages compared with permutation based test for high dimensional genetic or epigenetic data we propose a pseudolikelihood based expectation maximization test and show the proposed test follows a simple chi squared limiting distribution simulation studies show that the proposed test controls type i errors well and has better power compared to several current tests in particular the proposed test outperforms the commonly used tests under all simulation settings considered especially when there are variance differences between two groups the proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects

income distribution and inequality measurement the problem of extreme values we examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution estimation and inference can be dramatically affected especially when the tail of the income distribution is heavy even when standard bootstrap methods are employed however use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values

bootstrap recycling a monte carlo alternative to the nested bootstrap abstract a monte carlo algorithm is described that can be used in place of the nested bootstrap it is particularly advantageous when there is a premium on the number of bootstrap samples either because samples are hard to generate or because expensive computations are applied to each sample this recycling algorithm is useful because it enables inference procedures like prepivoting and bootstrap iteration in models where nested bootstrapping is computationally impractical implementation of the recycling algorithm is quite straightforward as a replacement of the double bootstrap for example bootstrap recycling involves two stages of sampling as does the double bootstrap the first stage of both algorithms is the same simulate from the fitted model in the second stage of recycling one batch of samples is simulated from one measure a measure dominating all the first stage fits these samples are recycled with each first stage sample to yield estimated adjustments to the original inference procedur

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

estimation and testing in constrained covariance component models a cutting plane algorithm is proposed for estimating variance and covariance components by maximum likelihood or restricted maximum likelihood enforcing the constraints that covariance matrices be positive semidefinite for tests of hypotheses involving these constrained estimates an asymptotic parametric bootstrap is proposed for approximating the distribution of the likelihood ratio test statistic although the bootstrap is generally inconsistent when the true parameter value is on the boundary of the feasible region the double bootstrap can be used to show that the ordinary bootstrap works well in certain problems

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

superconvergence of the velocity along the gauss lines in mixed finite element methods superconvergence for the velocity along the gauss lines is derived for the mixed finite element method for the second order elliptic equation in rectangular domains these estimates are based on the rectangular finite elements of raviart thomas type

superconvergence properties of optimal control problems an optimal control problem for a two dimensional 2 d elliptic equation is investigated with pointwise control constraints this paper is concerned with discretization of the control by piecewise constant functions the state and the adjoint state are discretized by linear finite elements approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state it is proved that these approximations have convergence order h2