The subject of this paper is to estimate adaptively the common probability density of independent, identically distributed random variables. The estimation is done at a fixed point , over the density functions that belong to the Sobolev class . We consider the adaptive problem setup, where the regularity parameter is unknown and varies in a given set . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.
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/} }
TY - JOUR AU - Butucea, Cristina TI - Exact adaptive pointwise estimation on Sobolev classes of densities JO - ESAIM: Probability and Statistics PY - 2001 DA - 2001/// SP - 1 EP - 31 VL - 5 PB - EDP-Sciences UR - http://www.numdam.org/item/PS_2001__5__1_0/ UR - https://zbmath.org/?q=an%3A0990.62032 UR - https://www.ams.org/mathscinet-getitem?mr=1845320 LA - en ID - PS_2001__5__1_0 ER -
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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