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

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

2008-03-20

arxiv.org/abs/0803.2999v1

Annals of Statistics 2007, Vol. 35, No. 6, 2589-2619

Mathematics

Statistics Theory

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

Scientific paper

10.1214/009053607000000415

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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