Semiparametric Bernstein-von Mises for the error standard deviation

Open Access
Authors
Publication date 2013
Journal Electronic Journal of Statistics
Volume | Issue number 7
Pages (from-to) 217-243
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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, nāˆ’āˆš-consistent estimation of the error standard deviation.
Document type Article
Language English
Published at https://doi.org/10.1214/13-EJS768
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