Optimal estimation in additive regression models

Joel Horowitz*, Jussi Klemelä, Enno Mammen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)271-298
Number of pages28
JournalBernoulli
Volume12
Issue number2
DOIs
StatePublished - Apr 2006

Keywords

  • Exact constants in nonparametric smoothing
  • Kernel estimators
  • Multivariate curve estimation
  • Nonparametric regression
  • Orthogonal series estimator
  • Smoothing splines

ASJC Scopus subject areas

  • Statistics and Probability

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