Nonparametric estimation of composite functions

Abstract : We study the problem of nonparametric estimation of a multivariate function $g:\bR^d\to\bR$ that can be represented as a composition of two unknown smooth functions $f:\bR\to\bR$ and $G:\bR^d\to\bR$. We suppose that $f$ and $G$ belong to some known smoothness classes of functions and we construct an estimator of $g$ which is optimal in a minimax sense for the sup-norm loss. The proposed methods are based on aggregation of linear estimators associated to appropriate local structures, and the resulting procedures are nonlinear with respect to observations.
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Journal articles
Annals of Statistics, Institute of Mathematical Statistics, 2009, 37 (3), pp.1360-1404. <10.1214/08-AOS611>


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Anatoli Juditsky, Oleg Lepski, Alexandre Tsybakov. Nonparametric estimation of composite functions. Annals of Statistics, Institute of Mathematical Statistics, 2009, 37 (3), pp.1360-1404. <10.1214/08-AOS611>. <hal-00148063>

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