English
Related papers

Related papers: Pitman Efficiency Lower Bounds for Multivariate Di…

200 papers

We develop a new rank-based approach for univariate two-sample testing in the presence of missing data which makes no assumptions about the missingness mechanism. This approach is a theoretical extension of the Wilcoxon-Mann-Whitney test…

Methodology · Statistics 2024-03-25 Yijin Zeng , Niall M. Adams , Dean A. Bodenham

Hotelling's $T^2$ test is a classical approach for discriminating the means of two multivariate normal samples that share a population covariance matrix. Hotelling's test is not ideal for high-dimensional samples because the eigenvalues of…

Statistics Theory · Mathematics 2022-06-07 Benjamin D. Robinson , Robert Malinas , Van Latimer , Beth Bjorkman Morrison , Alfred O. Hero

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…

Methodology · Statistics 2014-12-09 Ruth Heller , Yair Heller , Shachar Kaufman , Malka Gorfine

We study a stylized multiple testing problem where the test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We first show that, in the normal means model where the test statistics…

Statistics Theory · Mathematics 2016-04-27 Ery Arias-Castro , Shiyun Chen

In this paper, I propose a general procedure for multivariate distribution-free nonparametric testing derived from the concept of ranks that are based upon measure transportation in the context of multiple change point analysis. I will use…

Other Statistics · Statistics 2021-08-30 Amanda Ng

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…

Machine Learning · Statistics 2024-06-11 Gabriel Rioux , Apoorva Nitsure , Mattia Rigotti , Kristjan Greenewald , Youssef Mroueh

Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…

Statistics Theory · Mathematics 2015-08-05 Aaditya Ramdas , Sashank J. Reddi , Barnabas Poczos , Aarti Singh , Larry Wasserman

The robust rank-order test (Fligner and Policello, 1981) was designed as an improvement of the non-parametric Wilcoxon-Mann-Whitney U-test to be more appropriate when the samples being compared have unequal variance. However, it tends to be…

Methodology · Statistics 2020-09-08 Nirvik Sinha

Univariate concepts as quantile and distribution functions involving ranks and signs, do not canonically extend to $\mathbb{R}^d, d\geq 2$. Palliating that has generated an abundant literature. Chapter 1 shows that, unlike the many…

Methodology · Statistics 2020-02-28 Eustasio del Barrio , Juan A. Cuesta-Albertos , Marc Hallin , Carlos Matrán

As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…

Statistics Theory · Mathematics 2024-09-12 Li Tuobang

In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower…

Methodology · Statistics 2014-05-09 Radhendushka Srivastava , Ping Li , David Ruppert

Standard tests of the "no-treatment-effect" hypothesis for a comparative experiment include permutation tests, the Wilcoxon rank sum test, two-sample $t$ tests, and Fisher-type randomization tests. Practitioners are aware that these…

Methodology · Statistics 2015-09-11 Joseph B. Lang

We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…

Methodology · Statistics 2023-02-24 Xiaoyu Hu , Jing Lei

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…

Machine Learning · Computer Science 2020-02-18 Ilmun Kim , Aaditya Ramdas , Aarti Singh , Larry Wasserman

The basic motivation and primary goal of this paper is a qualitative evaluation of the performance of a new weighted statistic for a nonparametric test for stochastic dominance based on two samples, which was introduced in Ledwina and…

Statistics Theory · Mathematics 2018-06-07 Inglot Tadeusz , Ledwina Teresa , Ćmiel Bogdan

The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution,…

Statistics Theory · Mathematics 2019-02-26 Francisco Novoa-Muñoz

An explicit representation of an arbitrary zero-mean distribution as the mixture of (at-most-)two-point zero-mean distributions is given. Based in this representation, tests for (i) asymmetry patterns and (ii) for location without symmetry…

Statistics Theory · Mathematics 2007-06-13 Iosif Pinelis

Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard…

Statistics Theory · Mathematics 2025-03-26 Carles Domingo-Enrich , Raaz Dwivedi , Lester Mackey

The standard paired-sample testing approach in the multidimensional setting applies multiple univariate tests on the individual features, followed by p-value adjustments. Such an approach suffers when the data carry numerous features. A…

Machine Learning · Statistics 2023-09-29 Ioannis Bargiotas , Argyris Kalogeratos , Nicolas Vayatis

This research investigates how to determine whether two rankings come from the same distribution. We evaluate three hybrid tests: Wilcoxon's, Dietterich's, and Alpaydin's statistical tests combined with cross-validation (CV), each operating…

Methodology · Statistics 2022-02-14 Balázs R. Sziklai , Máté Baranyi , Károly Héberger