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.
Banerjee et al. (Wed,) studied this question.