Related papers: Analysis of Conditional Randomisation and Permutat…
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…
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…
We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…
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…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric…
Conditional independence tests are crucial across various disciplines in determining the independence of an outcome variable $Y$ from a treatment variable $X$, conditioning on a set of confounders $Z$. The Conditional Randomization Test…
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…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
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…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
In qualitative statistics, permutation tests are very popular, mainly because of their finite-sample exactness under exchangeability. However, in non-exchangeable settings, the covariance structure of permuted statistics typically differs…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine…
Randomization tests allow simple and unambiguous tests of null hypotheses, by comparing observed data to a null ensemble in which experimentally-controlled variables are randomly resampled. In behavioral and neuroscience experiments,…
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…