Generalized Linear Spectral Statistics of High-dimensional Sample Covariance Matrices and Its Applications
報(bào)告人簡(jiǎn)介
韓瀟，中國(guó)科學(xué)技術(shù)大學(xué)管理學(xué)院特任教授，研究方向?yàn)榇缶S隨機(jī)矩陣；高維統(tǒng)計(jì)推斷，入選國(guó)家創(chuàng)新人才計(jì)劃青年項(xiàng)目，主持青年基金項(xiàng)目與面上基金項(xiàng)目各一項(xiàng)
內(nèi)容簡(jiǎn)介
In this paper, we introduce the Generalized Linear Spectral Statistics (GLSS) of a high-dimensional sample covariance matrix. The joint asymptotic normality of GLSS associated with different test functions is established when the dimension and the sample size are comparable under weak assumptions. Subsequently, we propose a novel functional projection approach based on GLSS for hypothesis testing on eigenspaces of population-spiked covariance matrices. The theoretical accuracy of our results established for GLSS and the advantages of the newly suggested testing procedure are demonstrated through various numerical studies.
