Title: A test based on kernel density estimation for the eigenvalues in two-sample problem
Authors: Hidetoshi Murakami - Tokyo University of Science (Japan) [presenting]
Abstract: A hypothesis test is considered for the eigenvalue of covariance matrix in two-sample. Though the test statistic can be constructed by a parametric procedure, large samples are necessary to keep a significance level. Since it is difficult to derive the exact distribution of the eigenvalues of the covariance matrix, we can consider a nonparametric procedure. We propose a statistic based on kernel density estimation to test the hypothesis that the $j$th largest eigenvalues of a covariance matrix are equal in two-sample. By simulations, we investigate the actual significance level and the power of the procedure using several tests for variance, and find that the proposed test is suitable for various cases.