Displaying similar documents to “ Adaptive estimation of a quadratic functional of a density by model selection”

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2010)

ESAIM: Probability and Statistics

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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 x 0 ∈ ℝ , 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...