Related papers: Inefficient Best Invariant Tests
Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…
A multivariate one-sample location test based on the center-outward ranks and signs is considered, and two different testing procedures are proposed for centrally symmetric distributions. The first test is based on a random division of the…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We study a rank based univariate two-sample distribution-free test. The test statistic is the difference between the average of between-group rank distances and the average of within-group rank distances. This test statistic is closely…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
The theory of testing statistical functionals is developed for non-parametric two-sample problems. For differentiable real-valued statistical functionals, some tests for the one-sided and two-sided cases are proposed and studied. The…
In this paper, I construct a new test of conditional moment inequalities, which is based on studentized kernel estimates of moment functions with many different values of the bandwidth parameter. The test automatically adapts to the unknown…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…