In this article, a class of penalized likelihood probability density estimators is proposed and studied. The true log density is assumed to be a member of a reproducing kernel Hilbert space on a finite domain, not necessarily univariate, and the estimator is defined as the unique unconstrained minimizer of a penalized log likelihood functional in such a space. Under mild conditions, the existence of the estimator and the rate of convergence of the estimator in terms of the symmetrized Kullback-Leibler distance are established. To make the procedure applicable, a semiparametric approximation of the estimator is presented, which sits in an adaptive finite dimensional function space and hence can be computed in principle. The theory is developed in a generic setup and the proofs are largely elementary. Algorithms are yet to follow.
Publié le : 1993-03-14
Classification:
Density estimation,
penalized likelihood,
rate of convergence,
reproducing kernel Hilbert space,
semiparametric approximation,
smoothing splines,
62G07,
65D07,
65D10,
41A25,
41A65
@article{1176349023,
author = {Gu, Chong and Qiu, Chunfu},
title = {Smoothing Spline Density Estimation: Theory},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 217-234},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349023}
}
Gu, Chong; Qiu, Chunfu. Smoothing Spline Density Estimation: Theory. Ann. Statist., Tome 21 (1993) no. 1, pp. 217-234. http://gdmltest.u-ga.fr/item/1176349023/