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December 2007 Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions
Joel L. Horowitz, Enno Mammen
Ann. Statist. 35(6): 2589-2619 (December 2007). DOI: 10.1214/009053607000000415

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.

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Joel L. Horowitz. Enno Mammen. "Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions." Ann. Statist. 35 (6) 2589 - 2619, December 2007. https://doi.org/10.1214/009053607000000415

Information

Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62034
MathSciNet: MR2382659
Digital Object Identifier: 10.1214/009053607000000415

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 6 • December 2007
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