Bayesian Optimal Adaptive Estimation Using a Sieve prior

Julyan Arbel (), Ghislaine Gayraud () and Judith Rousseau ()
Additional contact information
Julyan Arbel: CREST
Ghislaine Gayraud: CREST
Judith Rousseau: CREST

No 2013-19, Working Papers from Center for Research in Economics and Statistics

Abstract: We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.

Keywords: adaptation; minimax criteria; nonparametric models; rate of contraction; sieve prior; white noise model (search for similar items in EconPapers)
Pages: 32
Date: 2013-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://crest.science/RePEc/wpstorage/2013-19.pdf Crest working paper version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:crs:wpaper:2013-19

Access Statistics for this paper

More papers in Working Papers from Center for Research in Economics and Statistics Contact information at EDIRC.
Bibliographic data for series maintained by Secretariat General () and Murielle Jules Maintainer-Email : murielle.jules@ensae.Fr.