• 演讲人： Qi-Man Shao（Southern University of Science and Technology ）
• 时间：2021年05月10日 周一上午10点
• 地点：紫金港校区行政楼1417报告厅
• 主办单位：浙江大学数据科学研究中心

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 talk, we will develop the central limit theorem 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. This talk is based on a joint work with Lan Gao, Yingying Fan and Jinchi Lv.

报告人简介

邵启满，南方科技大学统计与数据科学系创系系主任，讲席教授。主要从事概率统计基础理论的研究，他系统深入地发展了自正则化极限理论, 建立了自正则化大偏差、中偏差定理；发展完善了正态与非正态逼近的斯坦因方法，建立了随机浓度不等式和确定极限分布的基本方法；深入研究了相依变量极限理论，发展出了一系列重要的矩和概率不等式，建立了强逼近弱收敛等基础性工作。