Testing Independence via Spectral Moments

Assume that a matrix \(X:p\times n\) is matrix normally distributed and that the Kolmogorov condition , i.e., \(\lim _{n,p\rightarrow \infty }\frac{n}{p}=c>0\), holds. We propose a test for identity of the covariance matrix using a goodness-of-fit approach. Calculations are based on a recursive formula derived by Pielaszkiewicz et al. [19]. The test performs well regarding the power compared to presented alternatives, for both \(c<1\) or \(c\ge 1\).