Bayesian estimation in a high dimensional parameter framework Bosq, Denis Ruiz-Medina, María Dolores Asymptotic relative efficiency Bayesian estimation Hilbert valued Gaussian random variable Hilbert valued Poisson process 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. 2014-10-20T11:58:30Z 2014-10-20T11:58:30Z 2014 journal article 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] 1935-7524 http://hdl.handle.net/10481/33445 10.1214/14-EJS935 eng open access Institute of Mathematical Statistics