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--- seminars:stat:220303 [2022/02/23 12:53] – qyu
+++ seminars:stat:220303 [2022/03/02 13:09] (current) – qyu
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+<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
+<WRAP 70% center>
+^  **DATE:**|Thursday, March 3, 2022 |
+^  **TIME:**|1:15pm -- 2:15pm |
+^  **LOCATION:**|Zoom meeting |
+^  **SPEAKER:**|Geran Zhao, Binghamton University |
+^  **TITLE:**|Asymptotic distribution of high-dimensional distance correlation inference |
+</WRAP>
+\\
+<WRAP center box 80%>
+<WRAP centeralign>**Abstract**</WRAP>
+Distance correlation has become an increasingly popular tool
+for detecting the nonlinear dependence between a pair of potentially high-dimensional
+random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random
+vectors when only the sample size or the dimensionality diverges. Yet its
+asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit
+theorems and associated rates of convergence for a rescaled test statistic based on
+the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results
+reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of depen-
+dence, and further justify the capability of the rescaled distance
+correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results
+and finite-sample performance of the rescaled statistic are illustrated with
+several
+simulation examples and a blockchain application.
+</WRAP>