Semiparametric Bernstein–von Mises for the error standard deviation

Article, Other literature type English OPEN
de Jonge, René ; van Zanten, Harry (2013)
  • Publisher: The Institute of Mathematical Statistics and the Bernoulli Society
  • Journal: (issn: 1935-7524)
  • Related identifiers: doi: 10.1214/13-EJS768
  • Subject: Nonparametric regression | estimation of error variance | 62G09 | 62C10 | 62G20 | semiparametric Bernstein-von Mises | Bayesian inference
    arxiv: Statistics::Computation | Statistics::Theory | Statistics::Methodology

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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