报告人：Xiucai Ding
报告地点：腾讯会议ID:995 320 958;会议密码:1214
报告时间：2022年12月14日星期三10:00-11:00
报告摘要:
In this talk, I will report some recent results on the distributions of the largest few eigenvalues of sample covariance matrices under the generalized elliptical models. Consider the separable type sample covariance matrix Q = Σ^{1/2}XD^{2}X^{*}Σ ^{1/2} for some p × p positive definite deterministic matrix Σ, a random p × n matrix X and a random diagonal matrix D that is independent of X. This model finds important applications in statistics. For example, when X contains independent random vectors on the unit sphere, the model covers the elliptically distributed data. Moreover, when X contains i.i.d. centered normalized random variables, it can be either interpreted as a bootstrapping matrix or the Hessian matrix at certain layer in deep neural networks. We show that under various conditions on Σ and D, the extreme eigenvalues of Q can exhibit five different distributions: Frechet, Gumbel, Weibull, Tracy-Widom or Gaussian. Applications will be discussed.
This talk is based on a joint work with Jiahui Xie (NUS), Long Yu (SUFE) and Wang Zhou (NUS).
主讲人简介：
Xiucai Ding is currently an Assistant Professor of Statistics in the Universality of California, Davis. He got his PhD in statistics from the University of Toronto in 2018 and worked as a research associate at Duke University during 2018-2020. His research interests include high dimensional statistics, machine learning and manifold learning theory, and non-stationary time series and functional time series analysis.
