The Annals of Statistics

Improved Variable Window Kernel Estimates of Probability Densities

Peter Hall, Tien Chung Hu, and J. S. Marron

Full-text: Open access

Abstract

Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results can fail in important cases. In this paper, we characterize situations where the fast rate is valid, and also give rates for a variety of cases where they are slower. In addition, a modification of the usual variable window width estimator is proposed, which does have the earlier claimed rates of convergence.

Article information

Source
Ann. Statist., Volume 23, Number 1 (1995), 1-10.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324451

Digital Object Identifier
doi:10.1214/aos/1176324451

Mathematical Reviews number (MathSciNet)
MR1331652

Zentralblatt MATH identifier
0822.62026

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Adaptive methods bandwidth choice curve estimation nonparametric estimation smoothing

Citation

Hall, Peter; Hu, Tien Chung; Marron, J. S. Improved Variable Window Kernel Estimates of Probability Densities. Ann. Statist. 23 (1995), no. 1, 1--10. doi:10.1214/aos/1176324451. https://projecteuclid.org/euclid.aos/1176324451


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