On Azadkia–Chatterjee’s conditional dependence coefficient
By Hongjian Shi, Mathias Drton, Fang Han. Bernoulli, 2021
51 citations recorded by the source corpus.
In recent work, Azadkia and Chatterjee (2021) laid out an ingenious approach to defining 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 randomization 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 H\"older smooth alternatives. 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 (2022b). 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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/462bb0bfca6e0dfa2190f946767b8cc8536839de
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In Statistics and Probability
Citations in the corpus
- On boosting the power of Chatterjee’s rank correlation (2021, background): “Indeed, recent results have exhibited that a test of independence based on Proposition 2.2(ii) is inefficient in common classes of smooth alternatives; cf. Cao and Bickel (2020) and Shi et al. (2021b).”