On locally optimal tests for the mean direction of the Langevin distribution

A. SenGupta and S. Rao Jammalamadaka

Statistics & Probability Letters, 1991, vol. 12, issue 6, 537-544

Abstract: Hayakawa (1990) has very recently studied the behavior of the power for several large sample tests for the mean direction vector of the Langevin distribution. These tests are not known to possess any non-trivial optimal property. Here we derive some multiparameter locally optimal tests, e.g., best first and second directional derivative tests and locally most mean powerful tests. For the case when ?, the concentration parameter, is known, these tests are exact and some cut-off points are presented. For the case when ? is unknown, we propose C([alpha])-type tests which are expected to be asymptotically locally optimal. Some open problems are indicated.

Date: 1991
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