B0768
Title: Testing the order of a population spectral distribution for high-dimensional data
Authors: Yingli Qin - University of Waterloo (Canada) [presenting]
Abstract: Large covariance matrices play a fundamental role in high-dimensional statistics. Investigating the behavior of their eigenvalues can reveal informative structures of large covariance matrices. We propose to test the number of distinct population eigenvalues, i.e. the order of the Population Spectral Distribution (PSD). The proposed statistic is based upon a series of bias-reduced estimators of PSD moments. We develop the limiting distributions of our test statistic and the moment estimators. We also prove the $(n;p)-$strong consistency of these estimators, which are clearly demonstrated in our simulation study.
