The Annals of Statistics

Nonparametric estimation of an additive model with a link function

Joel L. Horowitz and Enno Mammen

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Abstract

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.

Article information

Source
Ann. Statist., Volume 32, Number 6 (2004), 2412-2443.

Dates
First available in Project Euclid: 7 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1107794874

Digital Object Identifier
doi:10.1214/009053604000000814

Mathematical Reviews number (MathSciNet)
MR2153990

Zentralblatt MATH identifier
1069.62035

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Additive models multivariate curve estimation nonparametric regression kernel estimates orthogonal series estimator

Citation

Horowitz, Joel L.; Mammen, Enno. Nonparametric estimation of an additive model with a link function. Ann. Statist. 32 (2004), no. 6, 2412--2443. doi:10.1214/009053604000000814. https://projecteuclid.org/euclid.aos/1107794874


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