On Empirical Bayes Testing for a Location Parameter in a Shifted Gamma Distribution

Abstract

Consider a location parameter θ in a shifted gamma distribution having a where is the fixed shape parameter. We study the two-action problem of testing against using the empirical Bayes approach. An empirical Bayes test is constructed. Under some mild conditions, is shown to be asymptotically optimal at a rate of order for where n is the number of past data available when the current decision problem is considered. The achieved rate of much improves the existing result in the literature.

Keywords:

• Asymptotically optimal
• Empirical Bayes testing
• Rate of convergence
• Regret.