主题：Asymptotics of Spiked Eigenvalues and Eigenvectors for Two Types of Random Matrices with Applications
主讲人：张志翔 宾夕法尼亚大学
主持人：刘一鸣 BETVLCTOR伟德官网下载
时间：2023年4月28日（周五）10：30-11：30
会议工具：腾讯会议（ID：803-746-349）
摘要
The spiked eigenvalues and eigenvectors of random matrices contain valuable information for statistical inference, and their asymptotic behavior is a central topic in random matrix theory. In this talk, I will investigate the asymptotic properties of the spiked eigenvalues and eigenvectors for two fundamental random matrix models: sample covariance matrices and signal-plus-noise matrices, under the high dimensional setting. The connection of the first-order limits of spiked eigenvalues and eigenvectors between these two models will also be considered.
Two applications that motivate the study of these two spiked models will be discussed. The first application proposes a new hypothesis testing statistic for testing the equality of large sample covariance matrices. The second aims to explore whether performing linear discriminant analysis on principal components is a reliable method, which is a common practice that shows good empirical performance but lacks theoretical guarantees.
主讲人简介
张志翔，2021年于新加坡南洋理工大学获得博士学位，师从潘光明教授。现于宾夕法尼亚大学统计与数据科学系进行博士后研究工作。主要研究方向有随机矩阵，高维统计及统计机器学习, 研究工作发表在 Annals of Statistics, IEEE Transactions on Information Theory, Bernoulli等期刊上。
校对|王国长
责编|麦嘉杰
初审|黄振
终审发布|郑贤
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