Semiparametric Bernstein-von Mises for the error standard deviation
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| Publication date | 2013 |
| Journal | Electronic Journal of Statistics |
| Volume | Issue number | 7 |
| Pages (from-to) | 217-243 |
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| Abstract | We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein-von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regression function and efficient, nāā-consistent estimation of the error standard deviation. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1214/13-EJS768 |
| Downloads |
Jonge-van_Zanten-van_ElectrJofStatistics_2013.pdf
(Final published version)
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