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Adaptive estimation with soft thresholding penalties
Author(s) -
Loubes Jean–Michel,
Van De Geer Sara
Publication year - 2002
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.t01-1-00212
Subject(s) - estimator , mathematics , thresholding , logarithm , nonparametric statistics , regression , function (biology) , penalty method , adaptive estimator , statistics , mathematical optimization , computer science , artificial intelligence , mathematical analysis , image (mathematics) , evolutionary biology , biology
We show that various robust nonparametric regression estimators, such as the least absolute deviations estimator, can be made adaptive (up to logarithmic factors), by adding a soft thresholding type penalty to the loss function. As an example, we consider the situation where the roughness of the regression function is described by a single parameter p . The theory is complemented with a simulation study.