Inference for a constrained parameter in presence of an uncertain constraint

2018/06/07 by Marchand, Éric, Nicoleris, Theodoros
#62C20 #62F10 #62F15 #62F30 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1806.02594

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.

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