Adaptive estimation of and oracle inequalities for probability densities and characteristic functions
| dc.creator | Efromovich, Sam | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T12:19:35Z | |
| dc.date.available | 2026-07-07T12:19:35Z | |
| dc.description | The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift--finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type oracle inequalities have been suggested for a vast set of functions including analytic and Sobolev with any positive index as well as for Efromovich--Pinsker and Stein blockwise-shrinkage estimators. Is it possible to obtain similar results for a more interesting applied problem of density estimation and/or the dual problem of characteristic function estimation? The answer is ``yes.'' In particular, the obtained results include exact exponential-type oracle inequalities which allow to consider, for the first time in the literature, a simultaneous sharp-minimax estimation of Sobolev densities with any positive index (not necessarily larger than 1/2), infinitely differentiable densities (including analytic, entire and stable), as well as of not absolutely integrable characteristic functions. The same adaptive estimator is also rate minimax over a familiar class of distributions with bounded spectrum where the density and the characteristic function can be estimated with the parametric rate. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009053607000000965 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/0806.2909 | |
| dc.identifier | http://arxiv.org/abs/0806.2909 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 3, 1127-1155 | |
| dc.identifier | doi:10.1214/009053607000000965 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212807 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05 (Primary) 62G20 (Secondary) | |
| dc.title | Adaptive estimation of and oracle inequalities for probability densities and characteristic functions | |
| dc.type | text |