On Azadkia–Chatterjee’s conditional dependence coefficient

Hongjian Shi, Mathias Drton, Fang Han

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In recent work, Azadkia and Chatterjee (Ann. Statist. 49 (2021) 3070–3102) laid out an ingenious approach to defin-ing consistent measures of conditional dependence. Their fully nonparametric approach forms statistics based on ranks and nearest neighbor graphs. The appealing nonparametric consistency of the resulting conditional dependence measure and the associated empirical conditional dependence coefficient has quickly prompted follow-up work that seeks to study its statistical efficiency. In this paper, we take up the framework of conditional random-ization tests (CRT) for conditional independence and conduct a power analysis that considers two types of local alternatives, namely, parametric quadratic mean differentiable alternatives and nonparametric Hölder smooth al-ternatives. Our local power analysis shows that conditional independence tests using the Azadkia–Chatterjee coefficient remain inefficient even when aided with the CRT framework, and serves as motivation to develop variants of the approach; cf. Lin and Han (Biometrika 110 (2023) 283–299). As a byproduct, we resolve a conjecture of Azadkia and Chatterjee by proving central limit theorems for the considered conditional dependence coefficients, with explicit formulas for the asymptotic variances.

Original languageEnglish
Pages (from-to)851-877
Number of pages27
JournalBernoulli
Volume30
Issue number2
DOIs
StatePublished - May 2024

Keywords

  • Conditional independence
  • graph-based test
  • local power analysis
  • nearest neighbor graphs
  • rank-based test

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