Work

Semiparametric Bernstein–von Mises for the error standard deviation

Year: 2013

Type: article

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, $\sqrt{n}$-consistent estimation of the error standard deviation.

Source: Electronic Journal of Statistics

DOI: 10.1214/13-ejs768

Authors: René de Jonge, Harry van Zanten

Institutions: Eindhoven University of Technology, University of Amsterdam

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek