The Annals of Statistics
- Ann. Statist.
- Volume 35, Number 6 (2007), 2589-2619.
Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions
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.
Ann. Statist. Volume 35, Number 6 (2007), 2589-2619.
First available in Project Euclid: 22 January 2008
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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. https://projecteuclid.org/euclid.aos/1201012973.