Estimating the suspected larger of two normal means: Estimating the suspected larger...: C. Drew , É. Marchand.

For X 1 , X 2 independently and normally distributed with means θ 1 and θ 2 , variances σ 1 2 and σ 2 2 , we consider Bayesian inference about θ 1 with the difference θ 1 - θ 2 being lower-bounded by an uncertain m. We obtain a class of minimax Bayes estimators of θ 1 , based on a posterior distribution for (θ 1 , θ 2) ⊤ taking values on R 2 , which dominate the unrestricted MLE under squared error loss for θ 1 - θ 2 ≥ 0 . We also construct and study an ad hoc credible set for θ 1 with approximate credibility 1 - α and provide numerical evidence of its frequentist coverage probability closely matching the nominal credibility level. A spending function is incorporated which further increases the coverage. [ABSTRACT FROM AUTHOR]