Geodesic
Exact adaptive pointwise estimation on Sobolev classes of densities
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 1-31

Voir la notice de l'article provenant de la source Numdam

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 ∈ℝ, over the density functions that belong to the Sobolev class W n (β,L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

Classification : 62N01, 62N02, 62G20
Keywords: density estimation, exact asymptotics, pointwise risk, sharp adaptive estimator 
@article{PS_2001__5__1_0,
     author = {Butucea, Cristina},
     title = {Exact adaptive pointwise estimation on {Sobolev} classes of densities},
     journal = {ESAIM: Probability and Statistics},
     pages = {1--31},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1845320},
     zbl = {0990.62032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PS_2001__5__1_0/}
}
TY  - JOUR
AU  - Butucea, Cristina
TI  - Exact adaptive pointwise estimation on Sobolev classes of densities
JO  - ESAIM: Probability and Statistics
PY  - 2001
SP  - 1
EP  - 31
VL  - 5
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/item/PS_2001__5__1_0/
LA  - en
ID  - PS_2001__5__1_0
ER  - 
%0 Journal Article
%A Butucea, Cristina
%T Exact adaptive pointwise estimation on Sobolev classes of densities
%J ESAIM: Probability and Statistics
%D 2001
%P 1-31
%V 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/item/PS_2001__5__1_0/
%G en
%F PS_2001__5__1_0
Butucea, Cristina. Exact adaptive pointwise estimation on Sobolev classes of densities. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 1-31. http://geodesic.mathdoc.fr/item/PS_2001__5__1_0/