Semiparametric Bernstein–von Mises for the error standard deviation

R. Jonge, de, J.H. Zanten, van

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
44 Downloads (Pure)

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, n-v-consistent estimation of the error standard deviation.
Original languageEnglish
Pages (from-to)217-243
JournalElectronic Journal of Statistics
Volume7
Issue number1
DOIs
Publication statusPublished - 2013

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