文章基本信息

标题：Semiparametric Bernstein–von Mises for the error standard deviation
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作者：René de Jonge ; Harry van Zanten
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：217-243
DOI：10.1214/13-EJS768
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Nonparametric regression;Bayesian inference, estimation of error variance;semiparametric Bernstein-von Mises.