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ON A MONOTONE EMPIRICAL BAYES TEST PROCEDURE

IN GEOMETRIC MODEL

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TACHEN LIANG^{1} AND S. PANCHAPAKESAN^{2}

^{1} *Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.*

^{2} *Department of Mathematics, Southern Illinois University,*

Carbondale, IL 62901-4408, U.S.A.
(Received November 17, 1989; revised September 17, 1990)

**Abstract.**
A monotone empirical Bayes procedure
is proposed for testing *H*_{0}:
*theta* __>__ *theta*_{0} against *H*_{1}:*theta* < *theta*_{0}, where
*theta* is the parameter of a geometric distribution. The
asymptotic optimality of the test procedure is established
and the associated convergence rate is shown to be of
order *O*(exp(-*cn*)) for some positive constant *c*, where
*n* is the number of accumulated past experience
(observations) at hand.

*Key words and phrases*:
Bayes, empirical Bayes,
hypothesis testing, geometric, antitonic and isotonic
regression, asymptotic optimality, convergence rate.

**Source**
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