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Probability Theory and Related Fields

, Volume 152, Issue 1–2, pp 53–99 | Cite as

A semiparametric Bernstein–von Mises theorem for Gaussian process priors

  • Ismaël Castillo
Article

Abstract

This paper is a contribution to the Bayesian theory of semiparametric estimation. We are interested in the so-called Bernstein–von Mises theorem, in a semiparametric framework where the unknown quantity is (θ, f), with θ the parameter of interest and f an infinite-dimensional nuisance parameter. Two theorems are established, one in the case with no loss of information and one in the information loss case with Gaussian process priors. The general theory is applied to three specific models: the estimation of the center of symmetry of a symmetric function in Gaussian white noise, a time-discrete functional data analysis model and Cox’s proportional hazards model. In all cases, the range of application of the theorems is investigated by using a family of Gaussian priors parametrized by a continuous parameter.

Keywords

Bayesian non and semiparametrics Bernstein–von Mises Theorems Gaussian process priors Estimation of the center of symmetry Cox’s proportional hazards model 

Mathematics Subject Classification (2000)

62G05 62G20 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.CNRS, LPMA ParisParisFrance

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