The Annals of Statistics

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

Joel L. Horowitz and Enno Mammen

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Abstract

This paper discusses a nonparametric 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 one-dimensional 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.

Article information

Source
Ann. Statist. Volume 35, Number 6 (2007), 2589-2619.

Dates
First available in Project Euclid: 22 January 2008

Permanent link to this document
http://projecteuclid.org/euclid.aos/1201012973

Digital Object Identifier
doi:10.1214/009053607000000415

Mathematical Reviews number (MathSciNet)
MR2382659

Zentralblatt MATH identifier
1129.62034

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

Keywords
Generalized additive models multivariate curve estimation nonparametric regression empirical process methods penalized least squares smoothing splines

Citation

Horowitz, Joel L.; Mammen, Enno. Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Ann. Statist. 35 (2007), no. 6, 2589--2619. doi:10.1214/009053607000000415. http://projecteuclid.org/euclid.aos/1201012973.


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