Related papers: On Azadkia-Chatterjee's conditional dependence coe…

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 $X$…

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…

This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…

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…

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…

This paper introduces a novel test for conditional stochastic dominance (CSD) at specific values of the conditioning covariates, referred to as target points. The test is relevant for analyzing income inequality, evaluating treatment…

Tests of independence are an important tool in applications, specifically in connection with the detection of a relationship between variables; they also have initiated many developments in statistical theory. In the present paper we build…

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

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…

Chatterjee's rank correlation is a directed measure of association designed to detect whether one variable can be predicted as a function of another. While the original coefficient is naturally defined for real-valued data, circular data…

In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our…

So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…

We propose a new method to test conditional independence of two real random variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$. %with $F_{.|.}$ representing conditional distribution functions, The partial copula…

In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular…

A necessary and suffcient condition for Pitman's asymptotic relative effciency (ARE) of the Kendall and Spearman correlation statistics for the independence test to be 1 is given, in terms of certain smoothness and nondegeneracy properties…

Studying the multivariate extension of copula correlation yields a dimension reduction principle, which turns out to be strongly related with the `simple measure of conditional dependence' $T$ recently introduced by Azadkia & Chatterjee…