Mengyu Xu : L2 asymptotics for high-dimensional data

Posted by Ryan Martin , part of the Statistics and Data Science Seminar.

At

Oct. 15, 2014, 4 p.m.

In

SEO 636

Abstract

We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ 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 resampling calibration method to approximate the distributions of the $L^2$ norms. Our results are applied to multiple tests and inference of covariance matrix structures.