On minimax density estimation on \mathbb{R}}
Juditsky, Anatoli ; Lambert-Lacroix, Sophie
Bernoulli, Tome 10 (2004) no. 2, p. 187-220 / Harvested from Project Euclid
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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.
Publié le : 2004-04-14
Classification:  adaptive estimation,  minimax estimation,  nonparametric density estimation 
@article{1082380217,
     author = {Juditsky, Anatoli and Lambert-Lacroix, Sophie},
     title = {On minimax density estimation on \mathbb{R}}},
     journal = {Bernoulli},
     volume = {10},
     number = {2},
     year = {2004},
     pages = { 187-220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082380217}
}

Juditsky, Anatoli; Lambert-Lacroix, Sophie. On minimax density estimation on \mathbb{R}}. Bernoulli, Tome 10 (2004) no. 2, pp.  187-220. http://gdmltest.u-ga.fr/item/1082380217/