On convergence rates of monotone empirical bayes tests for the continuous one-parameter exponential family

Empirical Bayes tests for testing H_o: 0 < 0 against H₁: θ > 0 for the continu- ous one-parameter exponential family are considered. The loss function is piecewise linear. The monotonocity of the problem can be used to obtain both Bayes and empirical Bayes monotone rules for the problem. A Van Houwelingen (1976) - type monotone empirical Bayes test is studied in this paper. A new method of estimation of the pivotal unknown parameter is proposed. Rates of convergence of the corresponding unconditional regret are investigated. The limit distribution of the conditional regret is also derived.