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March, 1993 Smoothing Spline Density Estimation: Theory
Chong Gu, Chunfu Qiu
Ann. Statist. 21(1): 217-234 (March, 1993). DOI: 10.1214/aos/1176349023

Abstract

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.

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Chong Gu. Chunfu Qiu. "Smoothing Spline Density Estimation: Theory." Ann. Statist. 21 (1) 217 - 234, March, 1993. https://doi.org/10.1214/aos/1176349023

Information

Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0770.62030
MathSciNet: MR1212174
Digital Object Identifier: 10.1214/aos/1176349023

Subjects:
Primary: 62G07
Secondary: 41A25, 41A65, 65D07, 65D10

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 1 • March, 1993
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