Abstract
The problem of density estimation on \mathbb{R}} on the basis of an independent sample X1,..., XN with common density f is discussed. The behaviour of the minimax Lp risk, 1≤p≤∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is given. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator which attains (up to a logarithmic factor in N) the lower bounds involved. We show that the minimax risk depends on the parameter p when p<2+ 1/s.
Citation
Anatoli Juditsky. Sophie Lambert-Lacroix. "On minimax density estimation on \mathbb{R}}." Bernoulli 10 (2) 187 - 220, April 2004. https://doi.org/10.3150/bj/1082380217
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