Biometrika May 05, 2026

A Ball Divergence-Based Measure for Conditional Independence Testing With a Local Wild Bootstrap

Authors
Bhaswar B Bhattacharya Bilol Banerjee Anil K Ghosh
Research Topics
Hypothesis Testing
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
Author
Bilol Banerjee
Author
Anil K Ghosh
Author
Research Topics & Keywords
Hypothesis Testing
Research Area
Citation 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 }
}