Monotone empirical Bayes tests for a discrete normal distribution

Abstract

Abstract We study the two-action problem in a discrete normal distribution via the empirical Bayes approach. An empirical Bayes test δ n ∗ is constructed based on an estimator a n ∗ of the critical point aG of the Bayes test. The empirical Bayes test δ n ∗ possesses the monotonicity and the asymptotic optimality, and its regret converges to zero at an exponential-type rate of order O(exp(−nτG)), where τG is a positive number, depending on the unknown prior distribution G.