Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions

Joel L. Horowitz, Enno Mammen

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

This paper discusses a nonparametrie regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a onedimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion.

Original languageEnglish (US)
Pages (from-to)2589-2619
Number of pages31
JournalAnnals of Statistics
Volume35
Issue number6
DOIs
StatePublished - Dec 2007

Keywords

  • Empirical process methods
  • Generalized additive models
  • Multivariate curve estimation
  • Nonparametric regression
  • Penalized least squares
  • Smoothing splines

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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