Tests for a given linear structure of the mean direction of the langevin distribution |
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| Authors: | Yoko Watamori |
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| Institution: | (1) Department of Mathematics, Faculty of Science, Hiroshima University, Naka-ku, 730 Hiroshima, Japan |
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| Abstract: | This paper deals with Watson statistic T
w
and likelihood ratio (LR) statistic T
l
for testing hypothesis H
0s:   V (a given s-dimensional subspace) based on a sample of size n from a p-variate Langevin distribution M
p(,  ). Asymptotic expansions of the null and non-null distributions of T
w
and T
l
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 is unknown. |
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| Keywords: | Asymptotic expansion central limit theorem Langevin distribution likelihood ratio statistic Watson statistic power comparison |
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