A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix
Abbreviated Journal Title
J. Multivar. Anal.
principal components analysis; sums of eigenvalues; ROOTS; LIMIT; Statistics & Probability
For the test of sphericity, Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102] proposed a statistic which is robust against high dimensionality. In this paper, we consider a natural generalization of their statistic for the test that the smallest eigenvalues of a covariance matrix are equal. Some inequalities are obtained for sums of eigenvalues and sums of squared eigenvalues. These bounds permit LIS to obtain the asymptotic null distribution of our statistic, as the dimensionality and sample size go to infinity together. by using distributional results obtained by Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102]. Some empirical results Comparing our test with the likelihood ratio test are also given. (C) 2005 Elsevier Inc. All rights reserved.
Journal of Multivariate Analysis
"A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix" (2006). Faculty Bibliography 2000s. 6556.