Exact adaptive pointwise estimation on Sobolev classes of densities

Butucea, Cristina

Butucea, Cristina

ESAIM: Probability and Statistics, Volume 5 (2001), pp. 1-31.

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 $x_{0} \in ℝ$ , 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.

MR: 1845320 | Zbl: 0990.62032 | 1 citation in Numdam

Classification: 62N01, 62N02, 62G20
Keywords: density estimation, exact asymptotics, pointwise risk, sharp adaptive estimator

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     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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%A Butucea, Cristina
%T Exact adaptive pointwise estimation on Sobolev classes of densities
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Butucea, Cristina. Exact adaptive pointwise estimation on Sobolev classes of densities. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 1-31. http://www.numdam.org/item/PS_2001__5__1_0/

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