The paper “Central Limit Theories for High-Dimensional Dependent Data”, co-authored by Prof. Jinyuan Chang from Southwestern University of Finance and Economics, Prof. Xiaohui Chen from the University of Illinois at Urbana-Champaign, and Ph.D. student Mingcong Wu from Southwestern University of Finance and Economics, has been officially accepted by Bernoulli, an internationally renowned academic journal in probability and statistics.
Abstract
This paper investigates the Gaussian approximation problem of ultra-high dimensional dependent data, and provides the normal approximation error convergence speed of ultra-high dimensional random vector sums based on hyper rectangular sets, simple convex sets, and sparse convex sets under three frameworks: alpha mixing, m-dependent, and physical dependent. Among them, the theoretical results based on the alpha mixing dependency framework were obtained for the first time, and the results under the physical dependency framework improved the existing results. In order to apply theoretical results to practical ultra-high dimensional statistical inference problems, this paper also proposes a data-driven parametric bootstrap method. This paper demonstrates how the established theory can be applied to statistical inference problems of ultra-high dimensional dependent data through three examples.
Author Introduction
Jinyuan Chang is the Executive Director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics. He is a Guanghua Distinguished Professor, Doctoral Supervisor, recipient of the National Science Fund for Distinguished Young Scholars of China, a Distinguished Expert of Sichuan Province, and a member of the Sichuan Province Statistical Expert Advisory Committee. His research focuses on ultra-high dimensional data analysis and high-frequency financial data analysis.
Xiaohui Chen is an Associate Professor in the Department of Statistics at the University of Illinois at Urbana-Champaign. His research specializes in high-dimensional statistics and machine learning.
Mingcong Wu is a Ph.D. student in Statistics at the Joint Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics, under the supervision of Professor Jinyuan Chang. His research interests include ultra-high dimensional dependent data analysis and Gaussian approximation.
