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

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 ${x}_{0}\in ℝ$, over the density functions that belong to the Sobolev class ${W}_{n}\left(\beta ,L\right)$. We consider the adaptive problem setup, where the regularity parameter $\beta$ 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
Mots clés : 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},
zbl = {0990.62032},
mrnumber = {1845320},
language = {en},
url = {http://www.numdam.org/item/PS_2001__5__1_0/}
}
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Butucea, Cristina. Exact adaptive pointwise estimation on Sobolev classes of densities. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 1-31. http://www.numdam.org/item/PS_2001__5__1_0/

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