The consistency of automatic kernel density estimates
type: Item
instance of: scholarly article
title: The consistency of automatic kernel density estimates
zbMATH Open document ID: 0569.62032
author: Clark S. Penrod
author: Luc Devroye
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: In this article the authors investigate the Parzen-Rosenblatt kernel density estimator on \(R^ d\) with data-dependent smoothing factor. Sufficient conditions on the asymptotic behavior of the smoothing factor are given under which the estimate is pointwise consistent almost everywhere for all densities f to be estimated. When the smoothing factor is a function only of the sample size, the authors show that these conditions are also necessary, a generalization of results by Deheuvels. The consistency of various automatic kernel density estimates is a simple consequence of the theorems proved by the authors.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3909536
zbMATH Keywords: Parzen-Rosenblatt kernel density estimator
zbMATH Keywords: data-dependent smoothing factor
zbMATH Keywords: consistency
zbMATH Keywords: automatic kernel density estimates
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346789
OpenAlex ID: W2007468371
DOI: 10.1214/AOS/1176346789
description: scientific article; zbMATH DE number 3909536