Electronic Journal of Statistics

Semiparametric Bernstein–von Mises for the error standard deviation

René de Jonge and Harry van Zanten

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 217-243.

First available in Project Euclid: 24 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G09: Resampling methods
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62G20: Asymptotic properties

Nonparametric regression Bayesian inference estimation of error variance semiparametric Bernstein-von Mises


de Jonge, René; van Zanten, Harry. Semiparametric Bernstein–von Mises for the error standard deviation. Electron. J. Statist. 7 (2013), 217--243. doi:10.1214/13-EJS768. https://projecteuclid.org/euclid.ejs/1359041590

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