Distribution of LRC for testing sphericity of a complex multivariate Gaussian model

Abstract

In this paper, exact null distribution of the likelihood ratio criterion for testing sphericity structure in a complex multivariate normal covariance matrix is obtained in computable series form. The method of inverse Mellin transform and contour integration has been used. Certain special cases are given explicitly in terms of the hypergeometric functions.

Keywords

• exact distribution
• moments
• inverse Mellin transform
• series representation
• Meijer's G-function.