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 ∈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},
     year = {2001},
     publisher = {EDP Sciences},
     volume = {5},
     mrnumber = {1845320},
     zbl = {0990.62032},
     language = {en},
     url = {https://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. https://www.numdam.org/item/PS_2001__5__1_0/

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