SOME TESTS CONCERNING THE COVARIANCE MATRIX IN HIGH DIMENSIONAL DATA

摘要

In this paper, tests are developed for testing certain hypotheses on the covariance matrix Σ, when the sample size N = n +1 is smaller than the dimension p of the data. Under the condition that (tr Σ~i/p) exists and > 0, as p → ∞, i = 1,..., 8, tests are developed for testing the hypotheses that the covariance matrix in a normally distributed data is an identity matrix, a constant time the identity matrix (spherecity), and is a diagonal matrix. The asymptotic null and non-null distributions of these test statistics are given.