PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nonparametric estimation of composite functions.
Anatoli Juditsky, Oleg Lepski and Alexandre Tsybakov
Annals of Statistics 2007.


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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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3864
Deposited By:Alexandre Tsybakov
Deposited On:25 February 2008