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June 2000 Functional aggregation for nonparametric regression
Anatoli Juditsky, Arkadii Nemirovski
Ann. Statist. 28(3): 681-712 (June 2000). DOI: 10.1214/aos/1015951994

Abstract

We consider the problem of estimating an unknown function $f$ from $N$ noisy observations on a random grid. In this paper we address the following aggregation problem: given $M$ functions $f_1,\dots, f_M$, find an “aggregated ”estimator which approximates $f$ nearly as well as the best convex combination $f^*$ of $f_1,\dots, f_M$. We propose algorithms which provide approximations of $f^*$ with expected $L_2$ accuracy $O(N^{-1/4}\ln^{1/4} M$. We show that this approximation rate cannot be significantly improved. We discuss two specific applications: nonparametric prediction for a dynamic system with output nonlinearity and reconstruction in the Jones – Barron class.

Citation

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Anatoli Juditsky. Arkadii Nemirovski. "Functional aggregation for nonparametric regression." Ann. Statist. 28 (3) 681 - 712, June 2000. https://doi.org/10.1214/aos/1015951994

Information

Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62338
MathSciNet: MR1792783
Digital Object Identifier: 10.1214/aos/1015951994

Subjects:
Primary: 62G08, 62L20

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • June 2000
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