Pearson Chi-Squared Conditional Randomization Test

doi:10.1109/TIT.2025.3618595

Return

Pearson Chi-Squared Conditional Randomization Test

2025-12-01

PRE

Adel Javanmard *

Mohammad Mehrabi

DOI：10.1109/TIT.2025.3618595

Original

Original request for help

Save

Abstract

En 中文

Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable Y and another variable X, while controlling for the effect of a high-dimensional confounding variable Z. In this paper, we introduce a novel test, called 'Pearson Chi-squared Conditional Randomization' (PCR) test, which uses the distributional information on covariates X,Z and constructs randomizations to test conditional independence. PCR leverages the i.i.d-ness property of the observations to obtain high-resolution p-values with a very small number of conditional randomizations. We also provide a power analysis of the PCR test, which captures the effect of various parameters of the test, the sample size and the distance of the alternative from the set of null distributions, measured in terms of a notion called 'conditional relative density'. In addition, we propose two extensions of the PCR test, with important practical implications: (i) parameter-free PCR, which uses Bonferroni's correction to decide on a tuning parameter in the test; (ii) robust PCR, which avoids inflations in the size of the test when there is slight error in estimating the conditional law P-X|Z .

Keywords:

Testing

Computational modeling

Random variables

Data models

Business

Standards

Null space

Genomics

Extraterrestrial phenomena

Data science

Statistical inference