publication . Other literature type . Article . 2013

Semiparametric Bernstein–von Mises for the error standard deviation

Jonge, de, R.; Zanten, van, J.H.;
Open Access English
  • Published: 01 Jan 2013
  • Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
  • Country: Netherlands
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.
arXiv: Statistics::MethodologyStatistics::ComputationStatistics::Theory
free text keywords: Nonparametric regression, Bayesian inference, estimation of error variance, semiparametric Bernstein-von Mises, 62G09, 62C10, 62G20
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