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April 2006 Optimal estimation in additive regression models
Joel Horowitz,, Jussi Klemelä, Enno Mammen
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Bernoulli 12(2): 271-298 (April 2006). DOI: 10.3150/bj/1145993975

Abstract

This paper is concerned with optimal estimation of the additive components of a nonparametric, additive regression model. Several different smoothing methods are considered, including kernels, local polynomials, smoothing splines and orthogonal series. It is shown that, asymptotically up to first order, each additive component can be estimated as well as it could be if the other components were known. This result is used to show that in additive models the asymptotically optimal minimax rates and constants are the same as they are in nonparametric regression models with one component.

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Joel Horowitz,. Jussi Klemelä. Enno Mammen. "Optimal estimation in additive regression models." Bernoulli 12 (2) 271 - 298, April 2006. https://doi.org/10.3150/bj/1145993975

Information

Published: April 2006
First available in Project Euclid: 25 April 2006

zbMATH: 1098.62043
MathSciNet: MR2218556
Digital Object Identifier: 10.3150/bj/1145993975

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 2 • April 2006
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