ON A MONOTONE EMPIRICAL BAYES TEST PROCEDURE IN GEOMETRIC MODEL

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

1Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

2Department 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} : θ ≥ θ_{0} against H_{1} : θ < θ_{0}, where θ 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.