Abstract: | In this paper we study the asymptotic behaviors of the likelihood ratio criterion (TL(s)), Watson statistic (TW(s)) and Rao statistic (TR(s)) for testing H0s: μ
(a given subspace) against H1s: μ
, based on a sample of size n from a p-variate Langevin distribution Mp(μ, κ) when κ is large. For the case when κ is known, asymptotic expansions of the null and nonnull distributions of these statistics are obtained. It is shown that the powers of these statistics are coincident up to the order κ−1. For the case when κ is unknown, it is shown that TR(s) TL(s) TW(s) in their powers up to the order κ−1. |