We study the Bayesian approach to nonparametric function estimation
problems such as nonparametric regression and signal estimation. We consider
the asymptotic properties of Bayes procedures for conjugate (= Gaussian)
priors.
¶ We show that so long as the prior puts nonzero measure on the very
large parameter set of interest then the Bayes estimators are not satisfactory.
More specifically, we show that these estimators do not achieve the correct
minimax rate over norm bounded sets in the parameter space. Thus all Bayes
estimators for proper Gaussian priors have zero asymptotic efficiency in this
minimax sense.
¶ We then present a class of priors whose Bayes procedures attain the
optimal minimax rate of convergence. These priors may be viewed as compound, or
hierarchical, mixtures of suitable Gaussian distributions.
Publié le : 2000-04-15
Classification:
White noise,
nonparametric regression,
Bayes,
minimax,
conjugate priors,
62G07,
62A15,
62G20
@article{1016218229,
author = {Zhao, Linda H.},
title = {Bayesian aspects of some nonparametric problems},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 532-552},
language = {en},
url = {http://dml.mathdoc.fr/item/1016218229}
}
Zhao, Linda H. Bayesian aspects of some nonparametric problems. Ann. Statist., Tome 28 (2000) no. 3, pp. 532-552. http://gdmltest.u-ga.fr/item/1016218229/