Title: On some inference problems in high-dimensional factor models

Speaker:  Jianfeng Yao, The University of Hong Kong and University of  Rennes  1

Time: 2013.7.12（Friday） am10:30-11:30

Place:数学楼二楼学术报告厅

Abstract:

In this talk, I will give a short introduction to the general problem of estimation of a large covariance matrix. Next, the focus will be on a special class of so-called spiked covariance matrices that covers  in particular high-dimensional strict factor models.   First, the estimation problem of the noise variance will be discussed using high-dimensional observations.  Next,  we consider the goodness-of-fit test of a strict factor model  and derive new asymptotic distribution for the LR statistic under the high-dimensional setting.  Our approach is entirely based on recent advances  of the theory of random matrices, in particular those related to the eigenvalues distribution of a large and spiked sample covariance matrices.