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December 2005 Multivariate Bayesian function estimation
Jean-François Angers, Peter T. Kim
Ann. Statist. 33(6): 2967-2999 (December 2005). DOI: 10.1214/009053605000000705

Abstract

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries on the multivariate nonparametric regression function. The Bayesian approach then allows one to incorporate hierarchical Bayesian methods directly into the spectral structure, thus providing a symmetry-adaptive multivariate Bayesian function estimator. One can also diffuse away some prior information in which the limiting case is a smoothing spline on the manifold. This, together with the result that the smoothing spline solution obtains the minimax rate of convergence in the multivariate nonparametric regression problem, provides good frequentist properties for the Bayes estimators. An application to astronomy is included.

Citation

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Jean-François Angers. Peter T. Kim. "Multivariate Bayesian function estimation." Ann. Statist. 33 (6) 2967 - 2999, December 2005. https://doi.org/10.1214/009053605000000705

Information

Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62032
MathSciNet: MR2253110
Digital Object Identifier: 10.1214/009053605000000705

Subjects:
Primary: 62C10 , 62G08
Secondary: 41A15 , 58J90

Keywords: Bayes factor , comets , cross-validation , Eigenfunctions , Eigenvalues , Posterior , Sobolev Spaces , zeta function

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • December 2005
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