Statistics Department Seminar Series: Jinchi Lv, Kenneth King Stonier Chair in Business Administration & Professor of Data Sciences and Operations, University of Southern California Marshall, Professor of Mathematics, University of Southern California

Abstract:
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 dependence, 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. This is a joint work with Yingying Fan, Lan Gao and Qiman Shao.

Link to the paper:
https://arxiv.org/abs/1910.12970

Short bio ( http://faculty.marshall.usc.edu/jinchi-lv/):
Jinchi Lv is Kenneth King Stonier Chair in Business Administration and Professor in Data Sciences and Operations Department of the Marshall School of Business at the University of Southern California, Professor in Department of Mathematics at USC, and an Associate Fellow of USC Dornsife Institute for New Economic Thinking (INET). He received his Ph.D. in Mathematics from Princeton University in 2007. He was McAlister Associate Professor in Business Administration at USC from 2016-2019. His research interests include statistics, machine learning, data science, business applications, and artificial intelligence and blockchain.

His papers have been published in journals in statistics, economics, business, computer science, information theory, neuroscience, and biology, and one of them was published as a Discussion Paper in Journal of the Royal Statistical Society Series B (2008). He is the recipient of Fellow of American Statistical Association (2020), NSF Grant (2020), Fellow of Institute of Mathematical Statistics (2019), Member of USC University Committee on Appointments, Promotions, and Tenure (UCAPT, 2019-2020), USC Marshall Dean's Award for Research Impact (2017), Adobe Data Science Research Award (2017), Simons Foundation Grant (2016), the Royal Statistical Society Guy Medal in Bronze (2015), NSF Faculty Early Career Development (CAREER) Award (2010), USC Marshall Dean's Award for Research Excellence (2009), NSF Grant (2008), and Zumberge Individual Award from USC's James H. Zumberge Faculty Research and Innovation Fund (2008). He has served as an associate editor of the Annals of Statistics (2013-2018), Journal of Business & Economic Statistics (2018-present), and Statistica Sinica (2008-2016).

This seminar will be livestreamed via Zoom https://umich.zoom.us/j/94350208889
There will be a virtual reception to follow.