On Bayes minimax estimators for a normal mean with an uncertain constraint†

Éric Marchand and Theodoros Nicoleris

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 8, 1873-1883

Abstract: We describe a hierarchical Bayesian approach for inference about a parameter θ lower-bounded by α with uncertain α, derive some basic identities for posterior analysis about (θ,α), and provide illustrations for normal and Poisson models. For the normal case with unknown mean θ and known variance σ2, we obtain Bayes estimators of θ that take values on R, but that are equally adapted to a lower-bound constraint in being minimax under squared error loss for the constrained problem.

Date: 2021
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DOI: 10.1080/03610926.2019.1656251

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