Related papers: An Independence Test Based on Recurrence Rates. An…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
In this paper we develop a novel nonparametric framework to test the independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$, based on {\it…
We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
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…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
In this paper we explore the behaviour of dependent test statistics for testing of multiple hypothesis . To keep simplicity, we have considered a mixture normal model with equicorrelated correlation set up. With a simple linear…
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…
Tests of equality of copulas between two samples are introduced and studied using the empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a subsampling Bernstein…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
In this paper we use a well know method in statistics, the $\delta$-method, to provide an asymptotic distribution for the Mutual Information, and construct and independence test based on it. Interesting connections are found with the…
We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
Nonparametric rank tests for homogeneity and component independence are proposed, which are based on data compressors. For homogeneity testing the idea is to compress the binary string obtained by ordering the two joint samples and writing…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…