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On the robustness of posterior means

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  • Jiafeng Chen

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 variance bounded by $V$. Let $G_1$ be a possibly misspecified prior with zero mean and variance bounded by $V$. We show that the squared error Bayes risk of the posterior mean under $G_1$ is bounded, subjected to an additional tail condition on $G_1$, uniformly over $G_0, G_1, \sigma^2 > 0$.

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  • Jiafeng Chen, 2023. "On the robustness of posterior means," Papers 2303.08653, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2303.08653
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    File URL: http://arxiv.org/pdf/2303.08653
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    References listed on IDEAS

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    1. Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Dec 2024.
    2. repec:dau:papers:123456789/1908 is not listed on IDEAS
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