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2013 Semiparametric Bernstein–von Mises for the error standard deviation
René de Jonge, Harry van Zanten
Electron. J. Statist. 7: 217-243 (2013). DOI: 10.1214/13-EJS768

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, $\sqrt{n}$-consistent estimation of the error standard deviation.

Citation

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René de Jonge. Harry van Zanten. "Semiparametric Bernstein–von Mises for the error standard deviation." Electron. J. Statist. 7 217 - 243, 2013. https://doi.org/10.1214/13-EJS768

Information

Published: 2013
First available in Project Euclid: 24 January 2013

zbMATH: 1337.62087
MathSciNet: MR3020419
Digital Object Identifier: 10.1214/13-EJS768

Subjects:
Primary: 62G09
Secondary: 62C10, 62G20

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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