On optimality of Bayesian testimation in the normal means problem
| dc.creator | Abramovich, Felix | |
| dc.creator | Grinshtein, Vadim | |
| dc.creator | Pensky, Marianna | |
| dc.date | 2007-12-06 | |
| dc.date.accessioned | 2026-07-07T08:49:27Z | |
| dc.date.available | 2026-07-07T08:49:27Z | |
| dc.description | We consider a problem of recovering a high-dimensional vector $μ$ observed in white noise, where the unknown vector $μ$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of $l_0$-type penalties. The penalties are associated with various choices of the prior distributions $π_n(\cdot)$ on the number of nonzero entries of $μ$ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule which accommodates many of the known thresholding and model selection procedures as particular cases corresponding to specific choices of $π_n(\cdot)$. Furthermore, they achieve optimality in a rather general setting under very mild conditions on the prior. We also specify the class of priors $π_n(\cdot)$ for which the resulting estimator is adaptively optimal (in the minimax sense) for a wide range of sparse sequences and consider several examples of such priors. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009053607000000226 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/0712.0904 | |
| dc.identifier | http://arxiv.org/abs/0712.0904 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 5, 2261-2286 | |
| dc.identifier | doi:10.1214/009053607000000226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144305 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62C10 (Primary); 62C20, 62G05 (Secondary) | |
| dc.title | On optimality of Bayesian testimation in the normal means problem | |
| dc.type | text |