Related papers: Minimax Optimal Conditional Independence Testing
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…
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…
Investigation of the reversibility of the directional hierarchy in the interdependency among the notions of conditional independence, conditional mean independence, and zero conditional covariance, for two random variables X and Y given a…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
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…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
Testing the significance of a variable or group of variables $X$ for predicting a response $Y$, given additional covariates $Z$, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test…
Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…
We consider testing multivariate conditional independence between a response Y and a covariate vector X given additional variables Z. We introduce the Multivariate Sufficient Statistic Conditional Randomization Test (MS-CRT), which…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
A rational probability distribution on four binary random variables $X, Y, Z, U$ is constructed which satisfies the conditional independence relations $[X \mathrel{\text{$\perp\mkern-10mu\perp$}} Y]$, $[X…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…