SMOOTHING SPLINE DENSITY-ESTIMATION - THEORY

• 成果类型: Article
• 署名作者: GU, C; QIU, CF
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349023
• 发表日期: 1993
• 页码: 217-234
• 关键词: penalized likelihood; Cross-validation; regression

摘要

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.