EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Free access article

Issue ESAIM: PS
Volume 5, 2001
Page(s) 1 - 31
DOI 10.1051/ps:2001100

DOI: 10.1051/ps:2001100


ESAIM: P&S, May 2001, Vol. 5, pp. 1-31

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea

Université Paris 10, Modal'X, bâtiment G, 200 avenue de la République, 92001 Nanterre, France; (cbutucea@u-paris10.fr) and Université Paris 6, Laboratoire Probabilités et Modèles Aléatoires, 6 rue Clisson, 75013 Paris, France; (butucea@ccr.jussieu.fr)

(Received November 15, 2000. Revised April 9, 2001.)

Abstract
The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point $x_{0}\in \mathbb R$, over the density functions that belong to the Sobolev class $W_n(\beta ,L)$. We consider the adaptive problem setup, where the regularity parameter $\beta $ is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.


AMS Subject: 62N01, 62N02, 62G20.

Key words: Density estimation, exact asymptotics, pointwise risk, sharp adaptive estimator.


© EDP Sciences, SMAI 2001


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.