A Ball Divergence-Based Measure for Conditional Independence Testing With a Local Wild Bootstrap
Authors
Research Topics
Paper Information
-
Journal:
Biometrika -
DOI:
10.1093/biomet/asag027 -
Published:
May 05, 2026 -
Added to Tracker:
May 06, 2026
Abstract
Abstract In this paper we introduce a new measure of conditional dependence between two random vectors X and Y given another random vector Z using the ball divergence. Our measure characterizes conditional independence and does not require any moment assumptions. We propose an estimator of the measure using a kernel-averaging technique and derive its asymptotic distribution. Using this estimator, we construct a test for conditional independence based on a novel local wild bootstrap algorithm. Specifically, we design a double-bandwidth-based wild bootstrap algorithm that asymptotically controls the Type I error rate and gives a consistent test against a general class of alternatives. We illustrate the advantage of our method, both in terms of Type I error and power, in a range of simulation settings and also in a real-data example. A consequence of our theoretical results is a general framework for studying the asymptotic properties of a two-sample conditional V -statistic, which is of independent interest.
Author Details
Bhaswar B Bhattacharya
AuthorBilol Banerjee
AuthorAnil K Ghosh
AuthorResearch Topics & Keywords
Hypothesis Testing
Research AreaCitation Information
APA Format
Bhaswar B Bhattacharya
,
Bilol Banerjee
&
Anil K Ghosh
(2026)
.
A Ball Divergence-Based Measure for Conditional Independence Testing With a Local Wild Bootstrap.
Biometrika
, 10.1093/biomet/asag027.
BibTeX Format
@article{paper1161,
title = { A Ball Divergence-Based Measure for Conditional Independence Testing With a Local Wild Bootstrap },
author = {
Bhaswar B Bhattacharya
and Bilol Banerjee
and Anil K Ghosh
},
journal = { Biometrika },
year = { 2026 },
doi = { 10.1093/biomet/asag027 },
url = { https://doi.org/10.1093/biomet/asag027 }
}