(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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