“L2 Asymptotics for High-Dimensional Data”
Dr. Mengyu Xu, University of Chicago

Date: Thursday, November 20, 2014
Time: 4:00 PM – 5:00 PM
Location: 269 Everitt
Sponsor: Department of Statistics, Xiaohui Chen

Abstract:

We develop an asymptotic theory for L2 norms of sample mean vectors of high-dimensional data. An invariance principle for the L2 norms is derived under conditions that involve a delicate interplay between the dimension p, the sample size n and the moment condition. Under proper normalization, central and non-central limit theorems are obtained. To facilitate the related statistical inference, we propose a plug-in calibration method and a sub-sampling procedure to approximate the distributions of the L2 norms. Our results are applied to multiple tests and inference of covariance matrix structures.