Let $(X, Y)$ be a pair of random variables such that $X = (X_1,\cdots, X_J)$ ranges over $C = \lbrack 0, 1\rbrack^J$. The conditional distribution of $Y$ given $X = x$ is assumed to belong to a suitable exponential family having parameter $\eta \in \mathbb{R}$. Let $\eta = f(x)$ denote the dependence of $\eta$ on $x$. Let $f^\ast$ denote the additive approximation to $f$ having the maximum possible expected log-likelihood under the model. Maximum likelihood is used to fit an additive spline estimate of $f^\ast$ based on a random sample of size $n$ from the distribution of $(X, Y)$. Under suitable conditions such an estimate can be constructed which achieves the same (optimal) rate of convergence for general $J$ as for $J = 1$.
Publié le : 1986-06-14
Classification:
Exponential family,
nonparametric model,
additivity,
spline,
maximum quasi likelihood estimate,
rate of convergence,
62G20,
62G05
@article{1176349940,
author = {Stone, Charles J.},
title = {The Dimensionality Reduction Principle for Generalized Additive Models},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 590-606},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349940}
}
Stone, Charles J. The Dimensionality Reduction Principle for Generalized Additive Models. Ann. Statist., Tome 14 (1986) no. 2, pp. 590-606. http://gdmltest.u-ga.fr/item/1176349940/