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Mean-variance constrained priors have finite maximum Bayes risk in the normal location model
- Publication Year :
- 2023
- Publisher :
- arXiv, 2023.
-
Abstract
- Consider a normal location model $X \mid \theta \sim N(\theta, \sigma^2)$ with known $\sigma^2$. Suppose $\theta \sim G_0$, 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 $G_0, G_1, \sigma^2 > 0$.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0d57d09d16e34432d71571b16a8a5558
- Full Text :
- https://doi.org/10.48550/arxiv.2303.08653