Electronic Journal of Statistics

Bayesian estimation in a high dimensional parameter framework

Denis Bosq and María D. Ruiz-Medina

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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.

Article information

Electron. J. Statist., Volume 8, Number 1 (2014), 1604-1640.

First available in Project Euclid: 8 September 2014

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Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 65F15: Eigenvalues, eigenvectors

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


Bosq, Denis; Ruiz-Medina, María D. Bayesian estimation in a high dimensional parameter framework. Electron. J. Statist. 8 (2014), no. 1, 1604--1640. doi:10.1214/14-EJS935. https://projecteuclid.org/euclid.ejs/1410181226

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