Open Access
December 2004 Nonparametric estimation of an additive model with a link function
Joel L. Horowitz, Enno Mammen
Ann. Statist. 32(6): 2412-2443 (December 2004). DOI: 10.1214/009053604000000814


This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n−2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality. Moreover, the estimator has an oracle property. The asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.


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Joel L. Horowitz. Enno Mammen. "Nonparametric estimation of an additive model with a link function." Ann. Statist. 32 (6) 2412 - 2443, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1069.62035
MathSciNet: MR2153990
Digital Object Identifier: 10.1214/009053604000000814

Primary: 62G08
Secondary: 62G20

Keywords: Additive models , Kernel estimates , multivariate curve estimation , Nonparametric regression , orthogonal series estimator

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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