on the behavior of randomization tests without a group invariance assumption abstract fisher s randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions for example the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations on the other hand fisher s randomization construction is not applicable in this example unless the underlying populations differ only in location in general the basis for the randomization construction is invariance of the probability distribution of the data under a transformation group it is the goal of this article to understand the robustness properties of randomization tests by studying their asymptotic validity in situations where the basis for their construction breaks down here asymptotic validity refers to whether the probability of a type i error tends asymptotically to the nominal level in particula

superconvergent derivative recovery for lagrange triangular elements of degree p on unstructured grids in this paper we develop a postprocessing derivative recovery scheme for the finite element solution u h on general unstructured but shape regular triangulations in the case of continuous piecewise polynomials of degree p geq 1 by applying the global l 2 projection q h and a smoothing operator s h the recovered p th derivatives s h m q h partial p u h superconverge to the exact derivatives partial p u based on this technique we are able to derive a local error indicator depending only on the geometry of corresponding element and the p 1 st derivatives approximated by partial s h m q h partial p u h we provide several numerical examples illustrating the effectiveness of our schemes we also observe that higher order elements are likely to require more conservative refinement strategies to create meshes corresponding to optimal orders of convergence

confidence bands for a distribution function using the bootstrap abstract we first discuss the construction of bootstrap confidence bands for the distribution function f of a population for simple random sampling but do not assume that f is continuous the known alternative approach is to use the quantiles from the tabled kolmogorov distribution this approach is known to be conservative it has already been shown in bickel and freedman 1981 that the bootstrap confidence band has the correct coverage probability asymptotically we show by simulation that the bootstrap works well for small samples and outperforms the conservative approach particularly for distributions that have small carriers we also investigate the analogous problem of finding bootstrap confidence bands for the distribution function f of a population for a more complicated situation stratified random sampling the conservative approach in the previous situation is extended to this case when sampling is with replacement we expect that it holds for sampling without replacement and the supports of

placebo inference on treatment effects when the number of clusters is small abstract i introduce a general fisher style randomization testing framework to conduct nearly exact inference about the lack of effect of a binary treatment in the presence of very few large clusters when the treatment effect is identified across clusters the proposed randomization test formalizes and extends the intuitive notion of generating null distributions by assigning placebo treatments to untreated clusters i show that under simple and easily verifiable conditions the placebo test leads to asymptotically valid inference in a very large class of empirically relevant models examples discussed explicitly are i least squares regression with cluster level treatment ii difference in differences estimation and iii binary choice models with cluster level treatment a simulation study and an empirical example are provided the proposed inference procedure is easy to implement and performs well with as few as three treated and three untreated clusters

a permutational step up method of testing multiple outcomes this paper describes a permutational step up multiple comparison procedure to adjust the p values from k related hypotheses the method is applicable when two groups of subjects are being compared on each of k outcomes it is related to the step down method of westfall and young 1993 resampling based multiple testing examples and methods for p value adjustment volume 1 and troendle 1995 journal of the american statistical association 90 370 378 and is an alternative to the analytic step up method of dunnett and tamhane 1992 journal of the american statistical association 87 162 170 which requires a specific distribution and correlation structure by conditioning on the data observed this permutational method avoids any specific distribution or correlation assumption it is shown very generally that the method asymptotically controls the familywise probability of a type i error

exact and asymptotically robust permutation tests given independent samples from p and q two sample permutation tests allow one to construct exact level tests when the null hypothesis is p q on the other hand when comparing or testing particular parameters of p and q such as their means or medians permutation tests need not be level or even approximately level in large samples under very weak assumptions for comparing estimators we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability in finite samples when the underlying distributions are identical a quite general theory is possible based on a coupling construction as well as a key contiguity argument for the binomial and hypergeometric distributions the ideas are broadly applicable and special attention is given to a nonparametric k sample behrens fisher problem whereby a permutation test is constructed which is exact level under the hypothesis of identical distributions but has asymptotic rejection probability under the more general null hypothesis of equality of means a monte carlo simulation study is performed 2010 msc subject classifications primary 62e20 secondary 62g10

dealing with interval scale data in data envelopment analysis abstract this paper considers the problem of interval scale data in the most widely used models of data envelopment analysis dea the ccr and bcc models radial models require inputs and outputs measured on the ratio scale our focus is on how to deal with interval scale variables especially when the interval scale variable is a difference of two ratio scale variables like profit or the decrease increase in bank accounts we suggest the use of these ratio scale variables in a radial dea model

structural comparison of data envelopment analysis and multiple objective linear programming the concept of efficiency as it applies to decision making units dmus solutions alternatives plays an important role both in data envelopment analysis dea and multiple objective linear programming molp despite this and other apparent similarities dea and molp research has developed separately we show that structurally the dea formulation to identify efficient units is quite similar to the molp model based on the reference point or the reference direction approach to generate efficient solutions dea and molp should not be seen as substitutes but rather as complements we show that they cross fertilize each other molp provides interesting extensions to dea and dea provides new areas of application to molp

efficiency analysis to incorporate interval scale data abstract we develop an approach to efficiency analysis to enable us to incorporate interval scale data in addition to ratio scale data our approach introduces a measure of inefficiency and identifies efficient units as is done in data envelopment analysis the basic idea in our approach is to find the best hyperplane separating the units that are better and worse than each unit best is defined in such a way that the number of not better units is maximal the efficiency measure is defined as a proportion of not better units to all units the results are invariant under a strictly increasing linear re scaling of any input or output variables thus zeroes or negative values do not cause problems for the analysis the approach is used to analyze the data of the research evaluation exercise recently carried out at the university of joensuu finland

asymptotically exact a posteriori error estimators part i grids with superconvergence in part i of this work we develop superconvergence estimates for piecewise linear finite element approximations on quasi uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms in particular we first show a superconvergence of the gradient of the finite element solution uh and to the gradient of the interpolant ui we then analyze a postprocessing gradient recovery scheme showing that q h nabla u h is a superconvergent approximation to nabla u here qh is the global l2 projection in part ii we analyze a superconvergent gradient recovery scheme for general unstructured shape regular triangulations this is the foundation for an a posteriori error estimate and local error indicators

multivariate and multiple permutation tests abstract in this article we consider the use of permutation tests for comparing multivariate parameters from two populations first the underlying properties of permutation tests when comparing parameter vectors from two distributions p and q are developed although an exact level test can be constructed by a permutation test when the fundamental assumption of identical underlying distributions holds permutation tests have often been misused indeed permutation tests have frequently been applied in cases where the underlying distributions need not be identical under the null hypothesis in such cases permutation tests fail to control the type 1 error even asymptotically however we provide valid procedures in the sense that even when the assumption of identical distributions fails one can establish the asymptotic validity of permutation tests in general while retaining the exactness property when all the observations are i i d in the multivariate testing problem for testing the global null hypothesis of equality of parameter vectors a modified hotelling s t 2 statistic as well as tests based on the maximum of studentized absolute differences are considered in the latter case a bootstrap prepivoting test statistic is constructed which leads to a bootstrapping after permuting algorithm then these tests are applied as a basis for testing multiple hypotheses simultaneously by invoking the closure method to control the familywise error rate lastly monte carlo simulation studies and an empirical example are presented

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

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

robust rank procedures for the behrens fisher problem abstract the problem of testing for equality of the medians of two populations is considered the standard distribution free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis a method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations the method is demonstrated using the mann whitney wilcoxon statistic

randomization tests under an approximate symmetry assumption this paper develops a theory of randomization tests under an approximate symmetry assumption randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis here by exhibits symmetry we mean that the distribution remains invariant under a group of transformations in this paper we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis an important application of this idea is in settings where the data may be grouped into a xed number of clusters with a large number of observations within each cluster in such settings we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions in particular our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster but also across clusters this approach enjoys several advantages over other approaches in these settings among other things it leads to a test that is asymptotically similar which as shown in a simulation study translates into improved power at many alternatives finally we use our results to revisit the analysis of angrist and lavy 2009 who examine the impact of a cash award on exam performance for low achievement students in israel

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

a flexible approach to ranking with an application to mba programs we develop a model for flexibly ranking multi dimensional alternatives units into preference classes via mixed integer programming we consider a linear aggregation model but allow the criterion weights to vary within pre specified ranges this allows the individual alternatives units to play to their strengths we illustrate the use of the model by considering the financial times global mba program rankings and discuss the implications we argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking providing an argument for sorting or what we call flexible ranking

randomization inference for difference in differences with few treated clusters abstract inference using difference in differences with clustered data requires care previous research has shown that when there are few treated clusters t tests based on cluster robust variance estimators crves severely overreject and different variants of the wild cluster bootstrap can either overreject or underreject dramatically we study two randomization inference ri procedures a procedure based on estimated coefficients may be unreliable when clusters are heterogeneous a procedure based on t statistics typically performs better although by no means perfectly under the null but at the cost of some power loss an empirical example demonstrates that ri procedures can yield inferences that differ dramatically from those of other methods

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

bootstrap and randomization tests of some nonparametric hypotheses in this paper the asymptotic behavior of some nonparametric tests is studied in situations where both bootstrap tests and randomization tests are applicable under fairly general conditions the tests are asymptotically equivalent in the sense that the resulting critical values and power functions are appropriately close this implies among other things that the difference in the critical functions of the tests evaluated at the observed data tends to 0 in probability randomization tests may be preferable since an exact desired level of the test may be obtained for finite samples examples considered are testing independence testing for spherical symmetry testing for exchangeability testing for homogeneity and testing for a change point

superconvergence of quadratic finite elements on mildly structured grids superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes for a large class of practically useful grids the finite element solution u h is proven to be superclose to the inter polant u i and as a result a postprocessing gradient recovery scheme for u h can be devised the analysis is based on a number of carefully derived identities in addition to its own theoretical interests the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods

some nonasymptotic results on resampling in high dimension ii multiple tests in the context of correlated multiple tests we aim to nonasymptotically control the family wise error rate fwer using resampling type procedures we observe repeated realizations of a gaussian random vector in possibly high dimension and with an unknown covariance matrix and consider the one and two sided multiple testing problem for the mean values of its coordinates we address this problem by using the confidence regions developed in the companion paper ann statist 2009 to appear which lead directly to single step procedures these can then be improved using step down algorithms following an established general methodology laid down by romano and wolf j amer statist assoc 100 2005 94 108 this gives rise to several different procedures whose performances are compared using simulated data

a permutation test for the regression kink design the regression kink rk design is an increasingly popular empirical method for estimating causal effects of policies such as the effect of unemployment benefits on unemployment duration using si

analysis of recovery type a posteriori error estimators for mildly structured grids some recovery type error estimators for linear finite elements are analyzed under o h 1 0 regular grids superconvergence of order o h 1 0 p is established for recovered gradients by three different methods as a consequence a posteriori error estimators based on those recovery methods are asymptotically exact

optimal permutation tests for the analysis of group randomized trials two facts complicate the comparison of interventions in group randomized trials grt s a family of clinical trials in which each member of a particular group receives the same treatment assignment first individual outcomes within each group are often correlated second the number of groups in a grt is often not sufficient to make asymptotic approximations possible therefore the tests used with methods such as generalized estimating equations gee and penalized quasi likelihood pql originally developed for longitudinal studies may not be valid as an alternative a class of permutation tests is derived to maximize the power of testing for an intervention effect in a grt while maintaining a nominal test size the test uses a statistic that is a weighted sum of residuals with the weights based on the group sizes and the variability of each individual outcome through simulation we demonstrate the importance of weights to a permutation test s power and compare the power of permutation tests ge

a randomization based perspective on analysis of variance a test statistic robust to treatment effect heterogeneity summary fisher randomization tests for neyman s null hypothesis of no average treatment effect are considered in a finite population setting associated with completely randomized experiments involving more than two treatments the consequences of using the f statistic to conduct such a test are examined and we argue that under treatment effect heterogeneity use of the f statistic in the fisher randomization test can severely inflate the type i error under neyman s null hypothesis we propose to use an alternative test statistic derive its asymptotic distributions under fisher s and neyman s null hypotheses and demonstrate its advantages through simulations

randomization tests for weak null hypotheses in randomized experiments the fisher randomization test frt is appropriate for any test statistic under a sharp null hypothesis that can recover all missing potential outcomes however it is often sought after to test a

the use of permutation tests for the analysis of parallel and stepped wedge cluster randomized trials we investigate the use of permutation tests for the analysis of parallel and stepped wedge cluster randomized trials permutation tests for parallel designs with exponential family endpoints have been extensively studied the optimal permutation tests developed for exponential family alternatives require information on intraclass correlation a quantity not yet defined for time to event endpoints therefore it is unclear how efficient permutation tests can be constructed for cluster randomized trials with such endpoints we consider a class of test statistics formed by a weighted average of pair specific treatment effect estimates and offer practical guidance on the choice of weights to improve efficiency we apply the permutation tests to a cluster randomized trial evaluating the effect of an intervention to reduce the incidence of hospital acquired infection in some settings outcomes from different clusters may be correlated and we evaluate the validity and efficiency of permutation test in such settings lastly we propose a permutation test for stepped wedge designs and compare its performance with mixed effect modeling and illustrate its superiority when sample sizes are small the underlying distribution is skewed or there is correlation across clusters copyright 2017 john wiley sons ltd