Monotone Empirical Bayes Tests for the Continuous One-Parameter Exponential Family
Monotone Empirical Bayes Tests for the Continuous One-Parameter Exponential Family
Let $\theta$ be the natural parameter of a continuous one-parameter exponential family. An empirical Bayes test is constructed for testing $\theta \leqq 0$ against $\theta > 0$ with a piecewise linear loss function. Since the problem is monotone, Bayes tests for a given prior distribution can be characterized by a …