Related papers: Optimal rates for independence testing via $U$-sta…

We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test…

Let ${\bf R}$ be the Pearson correlation matrix of $m$ normal random variables. The Rao's score test for the independence hypothesis $H_0 : {\bf R} = {\bf I}_m$, where ${\bf I}_m$ is the identity matrix of dimension $m$, was first…

Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…

Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…

We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…

For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

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 :…

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…

In 1948 Hoeffding devised a nonparametric test that detects dependence between two continuous random variables X and Y, based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic takes O(n log n)…

Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent…

Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…

We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null…

In this paper, we study the problems in the discrete Fourier transform (DFT) test included in NIST SP 800-22 released by the National Institute of Standards and Technology (NIST), which is a collection of tests for evaluating both physical…

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…

This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…