ASYMPTOTIC NONNULL DISTRIBUTION OF LRC FOR TESTING $H:\mu=\mu_0$; $E=\sigma^2 I_p$ IN GAUSSIAN POPULATION

In this paper asymptotic expansions of the nonnull distribution of the likelihood ratio statistic for testing $H:\mu=\mu_0$; $E=\sigma^2 I_p$, against alternatives which are close to $H$, for Gaussian population, have been derived.

NONNULL DISTRIBUTION OF LRC FOR TESTING HOMOGENEITY OF COVARIANCE MATRICES OF COMPLETELY SYMMETRIC GAUSSIAN MODELS

The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices of completely symmetric Gaussian models are obta.ined in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived under certain alternatives for unequal samples.