Bernoulli

  • Bernoulli
  • Volume 12, Number 2 (2006), 271-298.

Optimal estimation in additive regression models

Joel Horowitz,, Jussi Klemelä, and Enno Mammen

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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.

Article information

Source
Bernoulli, Volume 12, Number 2 (2006), 271-298.

Dates
First available in Project Euclid: 25 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1145993975

Digital Object Identifier
doi:10.3150/bj/1145993975

Mathematical Reviews number (MathSciNet)
MR2218556

Zentralblatt MATH identifier
1098.62043

Keywords
exact constants in nonparametric smoothing kernel estimators multivariate curve estimation nonparametric regression orthogonal series estimator smoothing splines

Citation

Horowitz,, Joel; Klemelä, Jussi; Mammen, Enno. Optimal estimation in additive regression models. Bernoulli 12 (2006), no. 2, 271--298. doi:10.3150/bj/1145993975. https://projecteuclid.org/euclid.bj/1145993975


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