The Annals of Statistics

On Global Properties of Variable Bandwidth Density Estimators

Peter Hall

Full-text: Open access

Abstract

It is argued that mean integrated squared error is not a useful measure of the performance of a variable bandwidth density estimator based on Abramson's square root law. The reason is that when the unknown density $f$ has even moderately light tails, properties of those tails drive the formula for optimal bandwidth, to the virtual exclusion of other properties of $f$. We suggest that weighted integrated squared error be employed as the performance criterion, using a weight function with compact support. It is shown that this criterion is driven by pointwise properties of $f$. Furthermore, weighted squared-error cross-validation selects a bandwidth which gives first-order asymptotic optimality of an adaptive, feasible version of Abramson's variable bandwidth estimator.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 762-778.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348655

Digital Object Identifier
doi:10.1214/aos/1176348655

Mathematical Reviews number (MathSciNet)
MR1165591

Zentralblatt MATH identifier
0785.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62H12: Estimation

Keywords
Cross-validation density estimation integrated squared error square root law variable bandwidth

Citation

Hall, Peter. On Global Properties of Variable Bandwidth Density Estimators. Ann. Statist. 20 (1992), no. 2, 762--778. doi:10.1214/aos/1176348655. https://projecteuclid.org/euclid.aos/1176348655


Export citation