Statistics and Data Science Seminar
Mengyu Xu
University of Chicago
L2 asymptotics for high-dimensional data
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.
Wednesday October 15, 2014 at 4:00 PM in SEO 636