ON A MONOTONE EMPIRICAL BAYES TEST PROCEDURE
IN GEOMETRIC MODEL

TACHEN LIANG1 AND S. PANCHAPAKESAN2

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 H0: theta > theta0 against H1:theta < theta0, 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.

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