Asymptotic nonnull distribution of likelihood ratio statistic for testing homogeneity of complex multivariate gaussian populations

Abstract

In this paper asymptotic expansion of the nonnull distribution of the likelihood ratio statistic for testing homogeneity of several multivariate complex Gaussian populations has been derived. Nonnull moments are derived under the assumption of equality of covariance matrices. The asymptotic nonnull distribution is derived under the sequence of local alternatives, using logarithmic expansion for gamma function and some results on zonal polynomials.

Keywords:

• Multivariate analysis
• special functions
• nonnull distribution
• zonal polynomials
• asymptotics
• likelihood-ratio test

AMS 1970 subject classification:

• Primary 62H10
• Secondary 62H05

^∗Part of this work was done while he was University Grants Commission Visiting Fellow at the University of Rajasthan.

^∗Part of this work was done while he was University Grants Commission Visiting Fellow at the University of Rajasthan.

Notes

^∗Part of this work was done while he was University Grants Commission Visiting Fellow at the University of Rajasthan.