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

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.

Published in at http://dx.doi.org/10.1214/009053607000000415 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Nonparametric Estimation of an Additive Model With a Link Function
• Smooth backfitting in generalized additive models
• Bandwidth selection for smooth backfitting in additive models
• A simple smooth backfitting method for additive models
• Nonparametric estimation of composite functions

Cited by in corpus (6)

• Nonparametric regression using deep neural networks with ReLU activation function
• Statistical inference for time-changed Lévy processes via composite characteristic function estimation
• Nonparametric estimation of composite functions
• Nonlinear generalization of the monotone single index model
• The ET Interview: Professor Joel L. Horowitz
• Deep Regression for Repeated Measurements