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Exact adaptive pointwise estimation on Sobolev classes of densities
- Journal: ESAIM: Probability and Statistics / Volume 5 / 2001
- Published online by Cambridge University Press: 15 August 2002, pp. 1-31
- Print publication: 2001
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View 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 $x_{0}\in \mathbb R$
, over the density
functions that belong to the Sobolev class Wn(β,L). We consider the
adaptive problem setup, where the regularity parameter β is unknown
and varies in a given set Bn. A sharp adaptive estimator is obtained,
and the explicit asymptotical constant, associated to its rate of
convergence is found.
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