On the robustness of posterior means
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arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929623012474880 |
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| author | Chen, Jiafeng |
| author_facet | Chen, Jiafeng |
| contents | Consider a normal location model $X \mid θ\sim N(θ, σ^2)$ with known $σ^2$. Suppose $θ\sim G_0$, 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 $G_0, G_1, σ^2 > 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08653 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the robustness of posterior means Chen, Jiafeng Statistics Theory Econometrics Theoretical Economics Consider a normal location model $X \mid θ\sim N(θ, σ^2)$ with known $σ^2$. Suppose $θ\sim G_0$, 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 $G_0, G_1, σ^2 > 0$. |
| title | On the robustness of posterior means |
| topic | Statistics Theory Econometrics Theoretical Economics |
| url | https://arxiv.org/abs/2303.08653 |