Physical Sciences Division, Department of Statistics
University of Chicago
“Asymptotic Theory for Quadratic Forms of High-Dimensional Data”
I will present an asymptotic theory for quadratic forms of sample mean vectors of high-dimensional data. An invariance principle for the quadratic forms 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 perform the related statistical inference, I will propose a plug-in calibration method and a re-sampling procedure to approximate the distributions of the quadratic forms. The results will be applied multiple tests and inference of covariance matrix structures.