Bayesian estimation in a high dimensional parameter framework
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Institute of Mathematical Statistics
Asymptotic relative efficiencyBayesian estimationHilbert valued Gaussian random variableHilbert valued Poisson process
Bosq, D.; Ruiz-Medina, M.D. Bayesian estimation in a high dimensional parameter framework. Electronic Journal of Statistics, 8(1): 1604-1640 (2014). [http://hdl.handle.net/10481/33445]
SponsorshipThis work has been supported in part by projects MTM2012-32674 of the DGI (co-funded with FEDER funds), MEC, Spain.
Sufficient conditions are derived for the asymptotic efficiency and equivalence of componentwise Bayesian and classical estimators of the infinite-dimensional parameters characterizing l2 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.