Permutation Test for Equality of Individual an Eigenvalue from a Covariance Matrix in High-Dimension

Abstract

A test statistic for examining the equality of an individual eigenvalue in two populations of high dimension is proposed. The asymptotic distribution of the proposed statistic is derived and the validity of the permutation test is discussed. Simulations were used to investigate the power of the suggested statistic. The proposed statistic is applied to hand measurement data on white and aboriginal Australians to test the equality of the eigenvalues.

Keywords:

• Eigenvalue
• High dimensional case
• Permutation test
• Principal component score

Mathematics Subject Classification:

• Multivariate analysis
• Nonparametric inference