Multivariate Bayesian function estimation
| dc.creator | Angers, Jean-François | |
| dc.creator | Kim, Peter T. | |
| dc.date | 2006-03-06 | |
| dc.date.accessioned | 2026-07-07T08:07:39Z | |
| dc.date.available | 2026-07-07T08:07:39Z | |
| dc.description | Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries on the multivariate nonparametric regression function. The Bayesian approach then allows one to incorporate hierarchical Bayesian methods directly into the spectral structure, thus providing a symmetry-adaptive multivariate Bayesian function estimator. One can also diffuse away some prior information in which the limiting case is a smoothing spline on the manifold. This, together with the result that the smoothing spline solution obtains the minimax rate of convergence in the multivariate nonparametric regression problem, provides good frequentist properties for the Bayes estimators. An application to astronomy is included. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053605000000705 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0603136 | |
| dc.identifier | http://arxiv.org/abs/math/0603136 | |
| dc.identifier | Annals of Statistics 2005, Vol. 33, No. 6, 2967-2999 | |
| dc.identifier | doi:10.1214/009053605000000705 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131001 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62C10, 62G08 (Primary) 41A15, 58J90 (Secondary) | |
| dc.title | Multivariate Bayesian function estimation | |
| dc.type | text |