{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:19:05Z","timestamp":1787170745140,"version":"build-2736575974"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper we introduce a new measure of conditional dependence between two random vectors $ {\\boldsymbol{X}} $ and $ {\\boldsymbol{Y}} $, given another random vector $ \\boldsymbol{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\u00a0I 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.<\/jats:p>","DOI":"10.1093\/biomet\/asag027","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T11:46:22Z","timestamp":1775648782000},"source":"Crossref","is-referenced-by-count":1,"title":["A ball divergence-based measure for conditional independence testing with a local wild bootstrap"],"prefix":"10.1093","volume":"113","author":[{"given":"Bilol","family":"Banerjee","sequence":"first","affiliation":[{"name":"Theoretical Statistics and Mathematics Unit, Indian Statistical Institute , 203 B. T. 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