A0504
Title: On eigenvalue distributions of large auto-covariance matrices
Authors: Wangjun Yuan - Department of Mathematics, University of Luxembourg (Luxembourg) [presenting]
Jianfeng Yao - The Chinese University of Hong Kong-Shenzhen (China)
Abstract: A limiting distribution for eigenvalues of a class of auto-covariance matrices was established. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original non-regularized auto-covariance matrices are non-invertible, thus introducing supplementary difficulties for studying their eigenvalues through Girko's Hermitization scheme. The key result is a new polynomial lower bound for a specific family of least singular values associated with a rank-defective quadratic function of a random matrix with independent and identically distributed entries. Another innovation is that the lag of the auto-covariance matrices can grow to infinity with the matrix dimension.
