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October 2011 Bernstein–von Mises theorems for Gaussian regression with increasing number of regressors
Dominique Bontemps
Ann. Statist. 39(5): 2557-2584 (October 2011). DOI: 10.1214/11-AOS912


This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of regressors increases with the sample size. Two kinds of Bernstein–von Mises theorems are obtained in this framework: nonparametric theorems for the parameter itself, and semiparametric theorems for functionals of the parameter. We apply them to the Gaussian sequence model and to the regression of functions in Sobolev and Cα classes, in which we get the minimax convergence rates. Adaptivity is reached for the Bayesian estimators of functionals in our applications.


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Dominique Bontemps. "Bernstein–von Mises theorems for Gaussian regression with increasing number of regressors." Ann. Statist. 39 (5) 2557 - 2584, October 2011.


Published: October 2011
First available in Project Euclid: 30 November 2011

zbMATH: 1231.62061
MathSciNet: MR2906878
Digital Object Identifier: 10.1214/11-AOS912

Primary: 62F15 , 62G20 , 62J05

Keywords: adaptive estimation , Bernstein–von Mises theorem , Nonparametric Bayesian statistics , posterior asymptotic normality , semiparametric Bayesian statistics

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 5 • October 2011
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