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Generalized t-tests are constructed under weaker than normal conditions. In the first part of this paper we assume only the symmetry (around zero) of the error distribution (i). In the second part we assume that the error distribution is a…

Statistics Theory · Mathematics 2016-08-16 Gábor J. Székely

We initiate the study of distribution testing for probability distributions over the edges of a graph, motivated by the closely related question of ``edge-distribution-free'' graph property testing. The main results of this paper are…

Data Structures and Algorithms · Computer Science 2026-03-25 Yumou Fei

In the literature, derivations of exact null distributions of rank-sum statistics is often avoided in cases where one or more ties exist in the data. By deriving the null distribution in the no-ties case with the aid of classical $q$-series…

Statistics Theory · Mathematics 2025-08-19 Andrew V. Sills

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

Data Structures and Algorithms · Computer Science 2020-09-15 Ilias Diakonikolas , Themis Gouleakis , Daniel M. Kane , John Peebles , Eric Price

Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…

Methodology · Statistics 2021-01-28 Marc Hallin , Gilles Mordant , Johan Segers

In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a…

Methodology · Statistics 2024-04-05 Kosuke Morikawa , Yoshikazu Terada , Jae Kwang Kim

When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…

Statistics Theory · Mathematics 2018-08-16 Matt Goldman , David M. Kaplan

Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…

Machine Learning · Statistics 2020-11-20 Charvi Rastogi , Sivaraman Balakrishnan , Nihar B. Shah , Aarti Singh

Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…

Methodology · Statistics 2023-11-21 Hoseung Song , Hao Chen

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…

Statistics Theory · Mathematics 2022-05-26 Ilmun Kim , Sivaraman Balakrishnan , Larry Wasserman

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…

Data Structures and Algorithms · Computer Science 2024-06-14 Gautam Chandrasekaran , Adam R. Klivans , Vasilis Kontonis , Konstantinos Stavropoulos , Arsen Vasilyan

For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the…

Methodology · Statistics 2020-03-11 Zongliang Hu , Tiejun Tong , Marc G. Genton

In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…

Methodology · Statistics 2021-08-17 Bruno Ebner , Shawn Liebenberg , Jaco Visagie

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…

Methodology · Statistics 2019-10-01 Shubhadeep Chakraborty , Xianyang Zhang

Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…

Methodology · Statistics 2025-06-23 Yichuan Bai , Lynna Chu

Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…

Computational Complexity · Computer Science 2026-04-07 Cynthia Dwork , Pranay Tankala

The win ratio is a general method of comparing locations of distributions of two independent, ordinal random variables, and it can be estimated without distributional assumptions. In this paper we provide a unified theory of win ratio…

In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…

Statistics Theory · Mathematics 2021-03-03 Bhaswar B. Bhattacharya

We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…

Data Structures and Algorithms · Computer Science 2025-04-15 Gleb Novikov