Adaptive estimation of stationary Gaussian fields

Abstract : We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as approximation sets for the distribution of X, we introduce a novel model selection procedure for spatial fields. For all neighborhoods m in a given collection M, this procedure first amounts to computing a covariance estimator of X within the GMRFs of neighborhood m. Then, it selects a neighborhood by applying a penalization strategy. The so-defined method satisfies a nonasymptotic oracle type inequality. If X is a GMRF, the procedure is also minimax adaptive to the sparsity of its neighborhood. More generally, the procedure is adaptive to the rate of approximation of the true distribution by GMRFs with growing neighborhoods.
Type de document :
Article dans une revue
Annals of Statistics, Institute of Mathematical Statistics, 2009, 38 (3), pp.36. 〈10.1214/09-AOS751〉
Liste complète des métadonnées

Littérature citée [9 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00353251
Contributeur : Nicolas Verzelen <>
Soumis le : vendredi 8 octobre 2010 - 13:50:20
Dernière modification le : mardi 23 mai 2017 - 11:25:01
Document(s) archivé(s) le : lundi 10 janvier 2011 - 11:45:42

Fichier

2010-Ver-GMRF.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Collections

Citation

Nicolas Verzelen. Adaptive estimation of stationary Gaussian fields. Annals of Statistics, Institute of Mathematical Statistics, 2009, 38 (3), pp.36. 〈10.1214/09-AOS751〉. 〈inria-00353251v3〉

Partager

Métriques

Consultations de la notice

133

Téléchargements de fichiers

69