Open Access
2014 Bayesian estimation in a high dimensional parameter framework
Denis Bosq, María D. Ruiz-Medina
Electron. J. Statist. 8(1): 1604-1640 (2014). DOI: 10.1214/14-EJS935

Abstract

Sufficient conditions are derived for the asymptotic efficiency and equivalence of componentwise Bayesian and classical estimators of the infinite-dimensional parameters characterizing $l^{2}$ valued Poisson process, and Hilbert valued Gaussian random variable models. Conjugate families are considered for the Poisson and Gaussian univariate likelihoods, in the Bayesian estimation of the components of such infinite-dimensional parameters. In the estimation of the functional mean of a Hilbert valued Gaussian random variable, sufficient and necessary conditions, that ensure a better performance of the Bayes estimator with respect to the classical one, are also obtained for the finite-sample size case. A simulation study is carried out to provide additional information on the relative efficiency of Bayes and classical estimators in a high-dimensional framework.

Citation

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Denis Bosq. María D. Ruiz-Medina. "Bayesian estimation in a high dimensional parameter framework." Electron. J. Statist. 8 (1) 1604 - 1640, 2014. https://doi.org/10.1214/14-EJS935

Information

Published: 2014
First available in Project Euclid: 8 September 2014

zbMATH: 1297.62188
MathSciNet: MR3263132
Digital Object Identifier: 10.1214/14-EJS935

Subjects:
Primary: 62M10 , 62M20
Secondary: 62C10 , 65F15

Keywords: Asymptotic relative efficiency , Bayesian estimation , Hilbert valued Gaussian random variable , Hilbert valued Poisson process

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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