(Received March 9, 1990; revised November 5, 1990)
Abstract. This paper deals with Watson statistic TW and likelihood ratio (LR) statistic TL for testing hypothesis H0s : mu \in V (a given s-dimensional subspace) based on a sample of size n from a p-variate Langevin distribution Mp(mu,kappa). Asymptotic expansions of the null and non-null distributions of TW and TL are obtained when n is large. Asymptotic expressions of those powers are also obtained. It is shown that the powers of them are coincident up to the order n-1 when kappa is unknown.
Key words and phrases: Asymptotic expansion, central limit theorem, Langevin distribution, likelihood ratio statistic, Watson statistic, power comparison.