a zero one law approach to the central limit theorem for the weighted bootstrap mean we develop a new technique to prove the conditional clt for the weighted bootstrap mean through 0 1 laws we show that this conditional clt can be derived from an unconditional one which easily arises conditioning with respect to the weights from the standard lindeberg clt

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

convex constrained programmes with unattained infima abstract we consider a problem of minimization of convex function f x over the convex region r where the objective function and the feasible region have a common direction of recession in cases when one of these directions is not in the constancy space of the objective function then the minimal solution is not achieved even if the function f x is bounded below over the region r many algorithms if applied to this class of programmes do not guarantee convergence to the global infimum our approach to this problem leads to derivation of the equation of the feasible parametrized curve c t such that the infimum of the logarithmic penalty function along this curve is equal to the global infimum of the objective function over the region r we show that if all functions defining the program are analytic then c t is also an analytic function the equation of the curve can be successfully used to determine the global infimum in particular unboundedness of the convex constrained programmes in cases when the application of classical methods such as the steepest descent method fails to converge to the global infimum

feasibility in reverse convex mixed integer programming abstract in this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints where some or all of the variables are integer in particular we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility cf that is constraints that may affect a feasibility status of the system after some perturbation of the right hand sides furthermore we will investigate properties of the irreducible infeasible sets and infeasibility sets showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system are subsets of the set cf of constraints critical to feasibility

efficiency and robustness in resampling it is known that the standard delete 1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean square error of a statistic in the i i d setting however this equivalence no longer holds in the linear regression model it turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous in fact we can divide all the commonly used resampling procedures for linear regression models into two types the e type the efficient ones like the bootstrap and the r type the robust ones like the jackknife thus the theory presented here provides a unified view of all the known resampling procedures in linear regression

a group theoretic approach to a family of 2 local finite groups constructed by levi and oliver we extend the notion of a p local finite group defined in blo03 to the notion of a p local group we define morphisms of p local groups obtaining thereby a category and we introduce the notion of a representation of a p local group via signalizer functors associated with groups we construct a chain g g 0 g 1 of 2 local finite groups via a representation of a chain g g 0 g 1 of groups such that g 0 is the 2 local finite group of the third conway sporadic group co 3 and for n 0 g n is one of the 2 local finite groups constructed by levi and oliver in lo02 we show that the direct limit g of g exists in the category of 2 local groups and that it is the 2 local group of the union of the chain g the 2 completed classifying space of g is shown to be the classifying space b di 4 of the exotic 2 compact group of dwyer and wilkerson dw93

wild bootstrap for quantile regression the existing theory of the wild bootstrap has focused on linear estimators in this note we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators as most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression a simulation study on median regression is carried out to compare various bootstrap methods with a simple finite sample correction the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points

a reduced gradient method for quadratic programs with quadratic constraints and lp constrained lp approximation problems abstract a dual algorithm is developed for solving a general class of nonlinear programs that properly contains all convex quadratic programs with quadratic constraints and l p constrained l p approximation problems the general dual program to be solved has essentially linear constraints but the objective function is nondifferentiable when certain variables equal zero modifications to the reduced gradient method for linearly constrained problems are presented that overcome the numerical difficulties associated with the nondifferentiable objective function these modifications permit blocks of variables to move to and away from zero on certain iterations even though the objective function is nondifferentiable at points having a block of variables equal to zero

deconstructing hopf spaces we characterize hopf spaces with finitely generated cohomology as an algebra over the steenrod algebra we deconstruct the original space into an h space y with finite mod p cohomology and a finite number of p torsion eilenberg mac lane spaces we give a precise description of homotopy commutative h spaces in this setting

bootstrapping m estimators in generalized autoregressive conditional heteroscedastic models summarywe consider the weighted bootstrap approximation to the distribution of a class of m estimators for the parameters of the generalized autoregressive conditional heteroscedastic model we prove that the bootstrap distribution given the data is a consistent estimate in probability of the distribution of the m estimator which is asymptotically normal we propose an algorithm for the computation of m estimates which at the same time is useful for computing bootstrap replicates from the given data our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and existing bootstrap methods for the generalized autoregressive conditional heteroscedastic model such as percentile t subsampling schemes since some familiar bootstrap schemes are special cases of the weighted bootstrap this paper thus provides a unified theory and algorithm for bootstrapping in generalized autoregressive conditional heteroscedastic models

controlled perturbations for quadratically constrained quadratic programs consider a minimization problem of a convex quadratic function of several variables over a set of inequality constraints of the same type of function the duel program is a maximization problem with a concave objective function and a set of constrains that are essentially linear however the objective function is not differentiable over the constraint region in this paper we study a general theory of dual perturbations and derive a fundamental relationship between a perturbed dual program and the original problem based on this relationship we establish a perturbation theory to display that a well controlled perturbation on the dual program can overcome the nondifferentiability issue and generate an optimal dual solution for an arbitrarily small number a simple linear program is then constructed to make an easy conversion from the dual solution to a corresponding optimal primal solution moreover a numerical example is included to illustrate the potential of this controlled perturbation scheme

the classification of p compact groups for p odd a p compact group as defined by dwyer and wilkerson is a purely homotopically defined p local analog of a compact lie group it has long been the hope and later the conjecture that these objects should have a classification similar to the classification of compact lie groups in this paper we finish the proof of this conjecture for p an odd prime proving that there is a one to one correspondence between connected p compact groups and finite reflection groups over the p adic integers we do this by providing the last and rather intricate piece namely that the exceptional compact lie groups are uniquely determined as p compact groups by their weyl groups seen as finite reflection groups over the p adic integers our approach in fact gives a largely self contained proof of the entire classification theorem for p odd

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

stratification and duality for homotopical groups abstract we generalize quillen s f isomorphism theorem quillen s stratification theorem the stable transfer and the finite generation of cohomology rings from finite groups to homotopical groups as a consequence we show that the category of module spectra over c b g f p is stratified and costratified for a large class of p local compact groups g including compact lie groups connected p compact groups and p local finite groups thereby giving a support theoretic classification of all localizing and colocalizing subcategories of this category moreover we prove that p compact groups admit a homotopical form of gorenstein duality

the sorted effects method discovering heterogeneous effects beyond their averages the partial ceteris paribus effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates despite the apparent importance of heterogeneity a common practice in modern empirical work is to largely ignore it by reporting average partial effects or at best average effects for some groups while average effects provide very convenient scalar summaries of typical effects by definition they fail to reflect the entire variety of the heterogeneous effects in order to discover these effects much more fully we propose to estimate and report sorted effects a collection of estimated partial effects sorted in increasing order and indexed by percentiles by construction the sorted effect curves completely represent and help visualize the range of the heterogeneous effects in one plot they are as convenient and easy to report in practice as the conventional average partial effects they also serve as a basis for classification analysis where we divide the observational units into most or least affected groups and summarize their characteristics we provide a quantification of uncertainty standard errors and confidence bands for the estimated sorted effects and related classification analysis and provide confidence sets for the most and least affected groups the derived statistical results rely on establishing key new mathematical results on hadamard differentiability of a multivariate sorting operator and a related classification operator which are of independent interest we apply the sorted effects method and classification analysis to demonstrate several striking patterns in the gender wage gap we find that this gap is particularly strong for married women ranging from 60 to 0 between the 2 and 98 percentiles as a function of observed and unobserved characteristics while the gap for never married women ranges from 40 to 20 the most adversely affected women tend to be married do not have college degrees work in sales and have high levels of potential experience

triangles of groups given a certain commutative diagram of groups and monomorphisms does there necessarily exist a group in which the given diagram is essentially a diagram of subgroups and inclusions in general the answer is negative but j corson and gersten and stallings have shown that in the case of a nonspherical triangle of groups the answer is positive this paper improves on these results by weakening the non sphericality requirement

quantile regression with censoring and endogeneity in this paper we develop a new censored quantile instrumental variable cqiv estimator and describe its properties and computation the cqiv estimator combines powell 1986 censored quantile regression cqr to deal with censoring with a control variable approach to incorporate endogenous regressors the cqiv estimator is obtained in two stages that are nonadditive in the unobservables the first stage estimates a nonadditive model with infinite dimensional parameters for the control variable such as a quantile or distribution regression model the second stage estimates a nonadditive censored quantile regression model for the response variable of interest including the estimated control variable to deal with endogeneity for computation we extend the algorithm for cqr developed by chernozhukov and hong 2002 to incorporate the estimation of the control variable we give generic regularity conditions for asymptotic normality of the cqiv estimator and for the validity of resampling methods to approximate its asymptotic distribution we verify these conditions for quantile and distribution regression estimation of the control variable our analysis covers two stage uncensored quantile regression with nonadditive first stage as an important special case we illustrate the computation and applicability of the cqiv estimator with a monte carlo numerical example and an empirical application on estimation of engel curves for alcohol

are discoveries spurious distributions of maximum spurious correlations and their applications over the last two decades many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool can the discoveries by such data mining approaches be spurious due to high dimensionality and limited sample size can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data to answer these questions we need to derive the distributions of the maximum spurious correlations given certain number of predictors namely the distribution of the correlation of a response variable y with the best s linear combinations of p covariates x even when x and y are independent when the covariance matrix of x possesses the restricted eigenvalue property we derive such distributions for both finite s and diverging s using gaussian approximation and empirical process techniques however such a distribution depends on the unknown covariance matrix of x hence we use the multiplier bootstrap procedure to approximate the unknown distributions and establish the consistency of such a simple bootstrap approach the results are further extended to the situation where residuals are from regularized fits our approach is then applied to construct the upper confidence limit for the maximum spurious correlation and testing exogeneity of covariates the former provides a baseline for guarding against false discoveries due to data mining and the latter tests whether our fundamental assumptions for high dimensional model selection are statistically valid our techniques and results are illustrated by both numerical examples and real data analysis

gaussian and bootstrap approximations for high dimensional u statistics and their applications this paper studies the gaussian and bootstrap approximations for the probabilities of a nondegenerate u statistic belonging to the hyperrectangles in mathbb r d when the dimension d is large a two step gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed subject to mild moment conditions on the kernel we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in mathbb r d that decays polynomially in sample size for a high dimensional scaling limit where the dimension can be much larger than the sample size we also provide computable approximation methods for the quantiles of the maxima of centered u statistics specifically we provide a unified perspective for the empirical bootstrap the randomly reweighted bootstrap and the gaussian multiplier bootstrap with the jackknife estimator of covariance matrix as randomly reweighted quadratic forms and we establish their validity we show that all three methods are inferentially first order equivalent for high dimensional u statistics in the sense that they achieve the same uniform rate of convergence over all d dimensional hyperrectangles in particular they are asymptotically valid when the dimension d can be as large as o e n c for some constant c in 0 1 7 the bootstrap methods are applied to statistical applications for high dimensional non gaussian data including i principled and data dependent tuning parameter selection for regularized estimation of the covariance matrix and its related functionals ii simultaneous inference for the covariance and rank correlation matrices in particular for the thresholded covariance matrix estimator with the bootstrap selected tuning parameter we show that for a class of sub gaussian data error bounds of the bootstrapped thresholded covariance matrix estimator can be much tighter than those of the minimax estimator with a universal threshold in addition we also show that the gaussian like convergence rates can be achieved for heavy tailed data which are less conservative than those obtained by the bonferroni technique that ignores the dependency in the underlying data distribution

bayesian bootstrap for proportional hazards models we propose two bayesian bootstrap extensions the binomial and poisson forms for proportional hazards models the binomial form bayesian bootstrap is the limit of the posterior distribution with a beta process prior as the amount of the prior information vanishes and thus can be considered as a default nonparametric bayesian analysis it is also the same as lo s bayesian bootstrap for censored data when covariates are absent the poisson form bayesian bootstrap is equivalent to the bayesian analysis with cox s profile likelihood when the baseline distribution is discrete thus when the data set has many ties simulation study suggests that the binomial form bayesian bootstrap performs better than standard frequentist procedures in the frequentist sense an advantage of the proposed bayesian bootstrap procedures over the standard bayesian analysis is conceptual and computational simplicity finally it is shown that both bayesian bootstrap posteriors are asymptotically equivalent to the sampling distribution of the maximum likelihood estimator

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

smooth minimum distance estimation and testing with conditional estimating equations uniform in bandwidth theory abstract to study the influence of a bandwidth parameter in inference with conditional moments we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth which can vary within a wide range including bandwidths independent of the sample size we study its behavior under misspecification we also propose an efficient version of our estimator we develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth s influence our new methods are simple to implement apply to non smooth problems and perform well in our simulations

homotopy nilpotency in p regular loop spaces we consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p completion of a product of finite numbers of spheres we determine the homotopy nilpotency of those loop spaces as an answer to this problem

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

weighted likelihood estimation under two phase sampling we develop asymptotic theory for weighted likelihood esti mators wle under two phase stratied sampling without replacement we also consider several variants of wle s involving estimated weights and calibration a set of empirical process tools are developed including a glivenko cantelli theorem a theorem for rates of convergence of z estimators and a donsker theorem for the inverse probability weighted em pirical processes under two phase sampling and sampling without replace ment at the second phase using these general results we derive asymptotic distributions of the wle of a nite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is es timable either at regular or non regular rates we illustrate these results and methods in the cox model with right censoring and interval censor ing we compare the methods via their asymptotic variances under both sampling without replacement and the more usual and easier to analyze assumption of bernoulli sampling at the second phase ams 2000 subject classications primary 62e20 secondary 62g20 62d99 62n01

evaluating prediction rules for t year survivors with censored regression models suppose that we are interested in establishing simple but reliable rules for predicting future t year survivors through censored regression models in this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate sensitivity and specificity and positive and negative predictive values specifically under various working models we derive consistent estimators for the above measures through substitution and cross validation estimation procedures furthermore we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified confidence intervals for example for the difference of the precision measures between two competing rules can then be constructed all of the proposals are illustrated with real examples and their finite sample properties are evaluated through a simulation study

bootstrapping robust estimates for clustered data in mixed models the use of robust estimates raises several interesting inferential challenges one of these challenges arises from the realization that the effect of contamination is to increase the variability in the data but robust estimates of variance components are usually smaller than their nonrobust counterparts the robust estimates reflect the variability of the bulk of the data which is not the same as the variability in the data generating process this means that the naive implementation of bootstrap procedures might not work in this article we consider several bootstrap procedures including random effect transformation and weighted bootstraps we give conditions for the asymptotic validity of the bootstraps and assess their performance via a small simulation study both the transformation and generalized cluster bootstrap perform well and are asymptotically valid under reasonable conditions

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

some nonasymptotic results on resampling in high dimension i confidence regions we study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure the random vector is supposed to be either gaussian or to have a symmetric and bounded distribution the dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non asymptotic control of the confidence level following ideas inspired by recent results in learning theory we consider two approaches the first based on a concentration principle valid for a large class of resampling weights and the second on a direct resampled quantile specifically using rademacher weights several intermediate results established in the approach based on concentration principles are of self interest we also discuss the question of accuracy when using monte carlo approximations of the resampled quantities we present an application of these results to the one sided and two sided multiple testing problem in which we derive several resampling based step down procedures providing a non asymptotic fwer control we compare our different procedures in a simulation study and we show that they can outperform bonferroni s or holm s procedures as soon as the observed vector has sufficiently correlated coordinates

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

a large sample study of the bayesian bootstrap on donne une justification asymptotique du bootstrap bayesien on obtient des resultats lies a l article de rubin 1981 dans le meme sens que bickel et freedman 1981 et singh 1981 se rapportant a l article d efron 1979

functional central limit theorems for single stage sampling designs for a joint model based and design based inference we establish functional central limit theorems for the horvitz thompson empirical process and the h ajek empirical process centered by their finite population mean as well as by their super population mean in a survey sampling framework the results apply to single stage unequal probability sampling designs and essentially only require conditions on higher order correlations we apply our main results to a hadamard differentiable statistical functional and illustrate its limit behavior by means of a computer simulation

central limit theorems and bootstrap in high dimensions this paper derives central limit and bootstrap theorems for probabilities that sums of centered high dimensional random vectors hit hyperrectangles and sparsely convex sets specifically we derive gaussian and bootstrap approximations for probabilities p n 1 2 ni 1xi a p n 1 2 i 1nxi a where x1 xnx1 xn are independent random vectors in rprp and aa is a hyperrectangle or more generally a sparsely convex set and show that the approximation error converges to zero even if p pn p pn as n n and p np n in particular pp can be as large as o ecnc o ecnc for some constants c c 0c c 0 the result holds uniformly over all hyperrectangles or more generally sparsely convex sets and does not require any restriction on the correlation structure among coordinates of xixi sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend only on a small subset of their arguments with hyperrectangles being a special case

second order global optimality conditions for convex composite optimization in recent years second order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established in this paper second order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition this result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification in particular second order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained 1998 the mathematical programming society inc published by elsevier science b v

distributional consistency of the lasso by perturbation bootstrap summarythe lasso is a popular estimation procedure in multiple linear regression we develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model we allow the underlying covariates to be either random or nonrandom and show that the proposed bootstrap method works irrespective of the nature of the covariates we also investigate finite sample properties of the proposed bootstrap method in a moderately large simulation study

analysis of least absolute deviation summary we develop a unified l 1 based analysis of variance type method for testing linear hypotheses like the classical l2 based analysis of variance the method is coordinate free in the sense that it is invariant under any linear transformation of the covariates or regression parameters moreover it allows singular design matrices and heterogeneous error terms a simple approximation using stochastic perturbation is proposed to obtain cut offvalues for the resulting test statistics both test statistics and distributional approximations can be computed using standard linear programming an asymptotic theory is derived for the method special cases of one and multi way analysis of variance and analysis of covariance models are worked out in detail the main results of this paper can be extended to general quantile regression extensive simulations show that the method works well in practical settings the method is also applied to a dataset from general social surveys

generic inference on quantile and quantile effect functions for discrete outcomes quantile and quantile effect qe functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation existing inference methods for these functions

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

bootstrap confidence sets under model misspecification a multiplier bootstrap procedure for construction of likelihood based confidence sets is considered for finite samples and a possible model misspecification theoretical results justify the bootstrap consistency for a small or moderate sample size and allow to control the impact of the parameter dimension p the bootstrap approximation works if p n is small the main result about bootstrap consistency continues to apply even if the underlying parametric model is misspecified under the so called small modeling bias condition in the case when the true model deviates significantly from the considered parametric family the bootstrap procedure is still applicable but it becomes a bit conservative the size of the constructed confidence sets is increased by the modeling bias we illustrate the results with numerical examples for misspecified constant and logistic regressions jel classification codes c13 c15

validity of dependent bootstrapping in finite populations abstract the traditional bootstrap resamples with replacement from the original sample observations to form arrays of row wise independent and identically distributed bootstrap random variables there are situations for example when sampling from finite populations where resampling without replacement provides a more realistic bootstrap procedure and produces dependent bootstrap random variables the desired properties of consistency and asymptotic validity are shown to hold for certain nonparametric dependent bootstrap estimators in addition it is shown that the smaller variation in dependent bootstrap estimators can be used to increase precision in some of the estimators

an algorithm to determine boundedness of quadratically constrained convex quadratic programmes abstract in this paper we present an algorithm which can be used to determine whether or not a convex quadratic objective function is bounded from below over a feasible region defined by convex quadratic constraints if there are m constraints and n variables the algorithm terminates after at most min m 1 n 1 iterations each iteration requires the identification of implicit equality constraints in a system of homogeneous linear inequality and equality constraints and the identification can be completed by the solution of linear programmes in addition the algorithm has the advantage of providing a mechanism to reduce both the number of constraints and the dimension of the problem

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

a new finite loop space at the prime two we construct a space bdi 4 whose mod 2 cohomology ring is the ring of rank 4 mod 2 dickson invariants the loop space on bdi 4 is the first example of an exotic finite loop space at 2 we conjecture that it is also the last one

a finite loop space not rationally equivalent to a compact lie group we construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact lie group hence providing a counterexample to a classical conjecture aided by machine calculation we verify that our counterexample is minimal i e that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact lie group extending the classical known bound of 5

the two sample problem for poisson processes adaptive tests with a non asymptotic wild bootstrap approach considering two independent poisson processes we address the question of testing equality of their respective intensities we first propose single tests whose test statistics are u statistics based on general kernel functions the corresponding critical values are constructed from a non asymptotic wild bootstrap approach leading to level alpha tests various choices for the kernel functions are possible including projection approximation or reproducing kernels in this last case we obtain a parametric rate of testing for a weak metric defined in the rkhs associated with the considered reproducing kernel then we introduce in the other cases an aggregation procedure which allows us to import ideas coming from model selection thresholding and or approximation kernels adaptive estimation the resulting multiple tests are proved to be of level alpha and to satisfy non asymptotic oracle type conditions for the classical l2 norm from these conditions we deduce that they are adaptive in the minimax sense over a large variety of classes of alternatives based on classical and weak besov bodies in the univariate case but also sobolev and anisotropic nikol skii besov balls in the multivariate case

anti concentration and honest adaptive confidence bands modern construction of uniform condence e and nickl 2010 this condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process equivalently for the supremum of a gaussian process with the same covariance function as that of the studentized empirical process the principal contribution of this paper is to remove the need for this classical condition we show that a considerably weaker sucient condi tion is derived from an anti concentration property of the supremum of the approximating gaussian process and we derive an inequality lead ing to such a property for separable gaussian processes we refer to the new condition as a generalized sbr condition our new result shows that the supremum does not concentrate too fast around any value we then apply this result to derive a gaussian multiplier bootstrap procedure for constructing honest condence bands for nonparametric density estimators this result can be applied in other nonparametric problems as well an essential advantage of our approach is that it ap plies generically even in those cases where the limit distribution of the supremum of the studentized empirical process does not exist or is un known this is of particular importance in problems where resolution levels or other tuning parameters have been chosen in a data driven fash ion which is needed for adaptive constructions of the condence bands furthermore our approach is asymptotically honest at a polynomial rate namely the error in coverage level converges to zero at a fast polynomial speed with respect to the sample size in sharp contrast the approach based on extreme value theory is asymptotically honest only at a logarithmic rate the error converges to zero at a slow loga rithmic speed finally of independent interest is our introduction of a new practical version of lepski s method which computes the optimal non conservative resolution levels via a gaussian multiplier bootstrap method

quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods abstract this paper shows that the conditional quantile treatment effect on the treated is identified under i a conditional distributional difference in differences assumption and ii a new assumption that the dependence the copula between the change in untreated potential outcomes and the initial level of untreated potential outcomes is the same for the treated group and untreated group we consider estimation and inference with discrete covariates and propose a uniform inference procedure based on the exchangeable bootstrap finally we estimate the effect of increasing the minimum wage on the distribution of earnings for subgroups defined by race gender and education

a method of analytic centers for quadratically constrained convex quadratic programs an interior point method is developed for maximizing a concave quadratic function under convex quadratic constraints the algorithm constructs a sequence of nested convex sets and finds their approximate centers using a partial newton step given the first convex set and its approximate center the total arithmetic operations required to converge to an approximate solution are of order o sqrt m m n n 2 ln varepsilon where m is the number of constraints n is the number of variables and varepsilon is determined by the desired tolerance of the optimal value and the size of the first convex set a method to initialize the algorithm is also proposed so that the algorithm can start from an arbitrary perhaps infeasible point

the classification of 2 compact groups we prove that any connected 2 compact group is classified by its 2 adic root datum and in particular the exotic 2 compact group di 4 constructed by dwyer wilkerson is the only simple 2 compact group not arising as the 2 completion of a compact connected lie group combined with our earlier work with moller and viruel for p odd this establishes the full classification of p compact groups stating that up to isomorphism there is a one to one correspondence between connected p compact groups and root data over the p adic integers as a consequence we prove the maximal torus conjecture giving a one to one correspondence between compact lie groups and finite loop spaces admitting a maximal torus our proof is a general induction on the dimension of the group which works for all primes it refines the andersen grodal moller viruel methods by incorporating the theory of root data over the p adic integers as developed by dwyer wilkerson and the authors furthermore we devise a different way of dealing with the rigidification problem by utilizing obstruction groups calculated by jackowski mcclure oliver in the early 1990s less

quadratically constrained convex quadratic programmes faulty feasible regions abstract we are concerned with the problem of minimizing a convex quadratic function subject to convex quadratic constraints in particular we are concerned with the application of the method of analytic centres to problems having a faulty feasible region i e a region that is either unbounded or not full dimensional each iteration of a method of centres must determine an analytic centre of a truncated feasible region if the feasible region is faulty then the truncated region may have no interior it may have no analytic centre it may have an infinity of centres or it may have a unique centre thus the difficulty caused by faulty feasible regions is that even when the problem has a solution the method of centres may fail typically faulty regions have been dealt with by the direct method of adding more constraints and variables often involving a big m constant our method is unique in that it results in a reduction in the number of constraints and effectively in the number of variables

unboundedness of a convex quadratic function subject to concave and convex quadratic constraints abstract we present conditions for the existence of upper and lower bounds on convex quadratic objective functions subject to concave and convex quadratic constraints we also present techniques for determining whether or not the conditions are satisfied

bootstrap consistency for general semiparametric m estimation consider m estimation in a semiparametric model that is characterized by a euclidean parameter of interest and an infinite dimensional nuisance parameter as a general purpose approach to statistical inferences the bootstrap has found wide applications in semiparametric m estimation and because of its simplicity provides an attractive alternative to the inference approach based on the asymptotic distribution theory the purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool we show that under general conditions the bootstrap is asymptotically consistent in estimating the distribution of the m estimate of euclidean parameter that is the bootstrap distribution asymptotically imitates the distribution of the m estimate we also show that the bootstrap confidence set has the asymptotically correct coverage probability these general conclusions hold in particular when the nuisance parameter is not estimable at root n rate and apply to a broad class of bootstrap methods with exchangeable bootstrap weights this paper provides a first general theoretical study of the bootstrap in semiparametric models

a directional mixed effects model for compositional expenditure data abstractcompositional data are vectors of proportions defined on the unit simplex and this type of constrained data occur frequently in government surveys it is also possible for the compositional data to be correlated due to the clustering or grouping of the observations within small domains or areas we propose a new class of the mixed model for compositional data based on the kent distribution for directional data where the random effects also have kent distributions one useful property of the new directional mixed model is that the marginal mean direction has a closed form and is interpretable the random effects enter the model in a multiplicative way via the product of a set of rotation matrices and the conditional mean direction is a random rotation of the marginal mean direction in small area estimation settings the mean proportions are usually of primary interest and these are shown to be simple functions of the marginal mean direction for estimation we apply a quasi likelihood method whic

efficient estimation for rank based regression with clustered data rank based inference is widely used because of its robustness this article provides optimal rank based estimating functions in analysis of clustered data with random cluster effects the extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations the performance of the proposed method is satisfactory even when the correlation structure is misspecified or when heteroscedasticity in variance is present finally a real dataset is analyzed for illustration

conditional quantile processes based on series or many regressors abstract quantile regression qr is a principal regression method for analyzing the impact of covariates on outcomes the impact is described by the conditional quantile function and its functionals in this paper we develop the nonparametric qr series framework covering many regressors as a special case for performing inference on the entire conditional quantile function and its linear functionals in this framework we approximate the entire conditional quantile function by a linear combination of series terms with quantile specific coefficients and estimate the function valued coefficients from the data we develop large sample theory for the qr series coefficient process namely we obtain uniform strong approximations to the qr series coefficient process by conditionally pivotal and gaussian processes based on these two strong approximations or couplings we develop four resampling methods pivotal gradient bootstrap gaussian and weighted bootstrap that can be used for inference on the entire qr series coefficient function we apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function such as the conditional quantile function itself its partial derivatives average partial derivatives and conditional average partial derivatives specifically we obtain uniform rates of convergence and show how to use the four resampling methods mentioned above for inference on the functionals all of the above results are for function valued parameters holding uniformly in both the quantile index and the covariate value and covering the pointwise case as a by product we demonstrate the practical utility of these results with an empirical example where we estimate the price elasticity function and test the slutsky condition of the individual demand for gasoline as indexed by the individual unobserved propensity for gasoline consumption

feasible partition problem in reverse convex and convex mixed integer programming abstract in this paper we consider the consistent partition problem in reverse convex and convex mixed integer programming in particular we will show that for the considered classes of convex functions both integer and relaxed systems can be partitioned into two disjoint subsystems each of which is consistent and defines an unbounded region the polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided