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Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear…

Methodology · Statistics 2026-05-06 Michael Wieck-Sosa , Michel F. C. Haddad , Aaditya Ramdas

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…

Statistics Theory · Mathematics 2025-03-19 Jialin Zhang , Zhiyi Zhang

This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment…

Methodology · Statistics 2025-11-06 Gregory Fletcher Cox , Xiaoxia Shi , Yuya Shimizu

Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…

Methodology · Statistics 2025-06-19 Kontemeniotis Nikolaos , Vargiakakis Rafail , Tsagris Michail

The aim of this paper is to study the matrix discrepancy problem. Assume that $\xi_1,\ldots,\xi_n$ are independent scalar random variables with finite support and $\mathbf{u}_1,\ldots,\mathbf{u}_n\in \mathbb{C}^d$. Let $\mathcal{C}_0$ be…

Combinatorics · Mathematics 2021-05-25 Jiaxin Xie , Zhiqiang Xu , Ziheng Zhu

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two…

Information Theory · Computer Science 2020-01-24 Sadaf Salehkalaibar , Michele Wigger , Roy Timo

We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.

Probability · Mathematics 2011-07-05 Mingshang Hu

We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…

Data Structures and Algorithms · Computer Science 2025-11-05 Shivam Garg , Chirag Pabbaraju , Kirankumar Shiragur , Gregory Valiant

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in $L_1$-norm. In…

Statistics Theory · Mathematics 2021-01-20 Joseph Lam-Weil , Alexandra Carpentier , Bharath K. Sriperumbudur

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…

Methodology · Statistics 2023-04-19 Yukun Song , Carey E. Priebe , Minh Tang

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Data Structures and Algorithms · Computer Science 2025-06-05 Jan Seyfried , Sayantan Sen , Marco Tomamichel

This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…

Methodology · Statistics 2023-08-03 Dachuan Chen , Decai Liang , Long Feng

Correlated observations are ubiquitous phenomena in a plethora of scientific avenues. Tackling this dependence among test statistics has been one of the pertinent problems in simultaneous inference. However, very little literature exists…

Statistics Theory · Mathematics 2024-11-20 Monitirtha Dey

Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…

Methodology · Statistics 2022-03-02 Sara Elbouch , Olivier Michel , Pierre Comon

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…

Machine Learning · Statistics 2025-03-19 Boyang Sun , Yu Yao , Guang-Yuan Hao , Yumou Qiu , Kun Zhang

This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…

Machine Learning · Statistics 2025-06-11 Cencheng Shen , Yuexiao Dong

This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…

Statistics Theory · Mathematics 2023-10-31 Ilmun Kim , Matey Neykov , Sivaraman Balakrishnan , Larry Wasserman

Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…

Machine Learning · Statistics 2018-06-05 Emilie Kaufmann , Wouter Koolen , Aurelien Garivier

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$,…

Machine Learning · Statistics 2018-04-10 Krzysztof Chalupka , Pietro Perona , Frederick Eberhardt

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $\epsilon$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS,…

Data Structures and Algorithms · Computer Science 2023-08-23 Diptarka Chakraborty , Sourav Chakraborty , Gunjan Kumar