Volume 5, 2001
|Page(s)||1 - 31|
|Published online||15 August 2002|
Exact adaptive pointwise estimation on Sobolev classes of densities
Université Paris 10, Modal'X, bâtiment G,
200 avenue de la République,
92001 Nanterre, France;
Université Paris 6, Laboratoire Probabilités et Modèles Aléatoires, 6 rue
Clisson, 75013 Paris, France; email@example.com.
Revised: 9 April 2001
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 , over the density functions that belong to the Sobolev class Wn(β,L). We consider the adaptive problem setup, where the regularity parameter β 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.
Mathematics Subject Classification: 62N01 / 62N02 / 62G20
Key words: Density estimation / exact asymptotics / pointwise risk / sharp adaptive estimator.
© EDP Sciences, SMAI, 2001
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