Xuming He (Chair)

Abstract

Chatterjee (2019) (see also Dette et al., 2013) introduced a novel simple rank-based measure of dependence between X and Y real, which is 0 iff X and Y are independent, and 1 iff Y=h(X) a.s. for some h. In a follow up of this work Azadkia and Chatterjee (2021) extended these results to conditional independence and applied them to variable selection. Subsequent work by Cao and Bickel (2020) and Shi, Drton and Han (2020) showed that, for testing independence, this statistic, when compared to classical procedures, such as those of Spearman or Blum, Kiefer and Rosenblatt (BKR) has no local power (ROC area=1/2 asymptotically) for many plausible departures. In this lecture we will analyze this behaviour and its sources completely.