光华讲坛——社会名流与企业家论坛第 6567 期

主 题：Robust estimation of number of factors in high dimensional factor modeling via Spearman's rank correlation matrix利用Spearman秩相关矩阵对高维因子模型中因子数量进行稳健估计

主讲人：南方科技大学统计与数据科学系李曾副教授

主持人：统计学院林华珍教授

时间：2023年9月15日（周五）上午10-11点

举办地点：柳林校区弘远楼408会议室

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Dr Li is currently an associate professor in the Department of Statistics and Data Science, Southern University of Science and Technology. Previously she was a postdoctoral fellow in the Department of Statistics at the Pennsylvania State University. Dr. Li obtained her Ph.D. degree from the Department of Statistics and Actuarial Science at the University of Hong Kong. Dr. Li’s research covers random matrix theory and high dimensional statistics.

李曾，南方科技大学统计与数据科学系副教授。2017年获得香港大学统计与精算学系博士学位，2017-2019年先后在美国华盛顿大学、宾夕法尼亚州立大学从事博士后研究工作，并于2019年入职南方科技大学。主要研究领域为随机矩阵理论、高维统计分析等，研究成果发表于The Annals of Statistics, Scandinavian Journal of Statistics 等国际统计学期刊。

内容简介：

Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman’s rank correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is applicable for scenarios where either the common factors or idiosyncratic errors follow heavy-tailed distributions. We prove that the proposed estimator is consistent under mild conditions. Numerical experiments also demonstrate the superiority of our estimator compared to existing methods, especially for the heavy-tailed case.

确定高维因素建模中的因子个数是必要的，但具有挑战性，特别是当数据是重尾的时候。在高维环境下，维数和样本量都成比例趋近于无穷大，本文基于Spearman秩相关矩阵的谱特性，引入了一种新的估计量。主讲人的估计器适用于共用因子或误差项遵循重尾分布的情况。主讲人证明了所提出的估计量在温和条件下是一致的。数值实验也证明了该估计方法与现有方法相比的优越性，特别是在重尾情况下。