Mean-variance constrained priors have finite maximum Bayes risk in the normal location model

03/15/2023

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by   Jiafeng Chen, et al.

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Consider a normal location model X |θ∼ N(θ, σ^2) with known σ^2. Suppose θ∼ G_0, where the prior G_0 has zero mean and unit variance. Let G_1 be a possibly misspecified prior with zero mean and unit variance. We show that the squared error Bayes risk of the posterior mean under G_1 is bounded, uniformly over G_0, G_1, σ^2 > 0.