Bayesian improvements of a MRE estimator of a bounded location parameter. (English) Zbl 1271.62046

Summary: We study the frequentist risk performance of Bayesian estimators of a bounded location parameter, and focus on conditions placed on the shape of the prior density guaranteeing dominance over the minimum risk equivariant (MRE) estimator. For a large class of even and logconcave densities, even convex loss functions, we demonstrate in a unified manner that symmetric priors which are bowled shaped and logconcave lead to Bayesian dominating estimators. The results generalize similar results obtained by E. Marchand and W. E. Strawderman [Ann. Inst. Stat. Math. 57, No. 1, 129–143 (2005; Zbl 1082.62029)] for the fully uniform prior, as well as those obtained by T. Kubokawa [Ann. Stat. 22, No. 1, 290–299 (1994; Zbl 0816.62021)] for squared error loss. Finally, we present a detailed example and several remarks.


62F15 Bayesian inference
62F10 Point estimation
62F30 Parametric inference under constraints
62C20 Minimax procedures in statistical decision theory
Full Text: DOI Euclid


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