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de Jonge, René; van Zanten, Harry (2013)
Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
Languages: English
Types: Article
Subjects: Nonparametric regression, estimation of error variance, 62G09, 62C10, 62G20, semiparametric Bernstein-von Mises, Bayesian inference

Classified by OpenAIRE into

arxiv: Statistics::Methodology, Statistics::Computation, Statistics::Theory
Identifiers:doi:10.1214/13-EJS768
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.

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