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.
Publié le : 2007-12-15
Classification:
Generalized additive models,
multivariate curve estimation,
nonparametric regression,
empirical process methods,
penalized least squares,
smoothing splines,
62G08,
62G20
@article{1201012973,
author = {Horowitz, Joel L. and Mammen, Enno},
title = {Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 2589-2619},
language = {en},
url = {http://dml.mathdoc.fr/item/1201012973}
}
Horowitz, Joel L.; Mammen, Enno. Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Ann. Statist., Tome 35 (2007) no. 1, pp. 2589-2619. http://gdmltest.u-ga.fr/item/1201012973/