Tests for the mean direction of the Langevin distribution with large concentration parameter

Yasunori Fujikoshi and Yoko Watamori

Journal of Multivariate Analysis, 1992, vol. 42, issue 2, 210-225

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: [mu] [set membership, variant] (a given subspace) against H1s: [mu] [negated set membership] , based on a sample of size n from a p-variate Langevin distribution Mp([mu], ?) when ? is large. For the case when ? 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 ?-1. For the case when ? is unknown, it is shown that TR(s) [greater, double equals] TL(s) [greater, double equals] TW(s) in their powers up to the order ?-1.

Keywords: asymptotic; expansion; Langevin; distribution; likelihood; ratio; criterion; Rao; statistic; power; comparison; Watson; statistic (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (2)

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