Presentation 1-4, 15:00~15:45.
Speaker
Koji Tsukuda (Kyushu University)
Title
Asymptotic distribution of the trace of the products of four high-dimensional Wishart matrices and its application
Abstract
This presentation investigates properties of the Wishart distribution, with a focus on the trace of products of four independent Wishart matrices. An explicit formula for the variance of this quantity is derived, and its asymptotic normality is established under a high-dimensional regime.
As an application, a statistical testing procedure is proposed for the common principal components hypothesis concerning two population covariance matrices in high-dimensional settings. The performance of the proposed test is evaluated through numerical experiments.
This work is based on the article: Tsukuda and Matsuura (2021, Journal of Multivariate Analysis 186, 104822).