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June, 1992 On Global Properties of Variable Bandwidth Density Estimators
Peter Hall
Ann. Statist. 20(2): 762-778 (June, 1992). DOI: 10.1214/aos/1176348655


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.


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Peter Hall. "On Global Properties of Variable Bandwidth Density Estimators." Ann. Statist. 20 (2) 762 - 778, June, 1992.


Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0785.62040
MathSciNet: MR1165591
Digital Object Identifier: 10.1214/aos/1176348655

Primary: 62G05
Secondary: 62H12

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 2 • June, 1992
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