Related papers: A Powerful Bootstrap Test of Independence in High …

Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly…

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…

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 :…

Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…

We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under…

We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

We study an independence test based on distance correlation for random fields $(X,Y)$. We consider the situations when $(X,Y)$ is observed on a lattice with equidistant grid sizes and when $(X,Y)$ is observed at random locations. We provide…

We propose a nonparametric test for serial independence that aggregates pairwise similarities of observations with lag-dependent weights. The resulting statistic is powerful to general forms of temporal dependence, including nonlinear and…

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…

The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…

We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…

Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…

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)…

We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…