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September, 1992 Variable Kernel Density Estimation
George R. Terrell, David W. Scott
Ann. Statist. 20(3): 1236-1265 (September, 1992). DOI: 10.1214/aos/1176348768


We investigate some of the possibilities for improvement of univariate and multivariate kernel density estimates by varying the window over the domain of estimation, pointwise and globally. Two general approaches are to vary the window width by the point of estimation and by point of the sample observation. The first possibility is shown to be of little efficacy in one variable. In particular, nearest-neighbor estimators in all versions perform poorly in one and two dimensions, but begin to be useful in three or more variables. The second possibility is more promising. We give some general properties and then focus on the popular Abramson estimator. We show that in many practical situations, such as normal data, a nonlocality phenomenon limits the commonly applied version of the Abramson estimator to bias of $O(\lbrack h / \log h\rbrack^2)$ instead of the hoped for $O(h^4)$.


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George R. Terrell. David W. Scott. "Variable Kernel Density Estimation." Ann. Statist. 20 (3) 1236 - 1265, September, 1992.


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

zbMATH: 0763.62024
MathSciNet: MR1186249
Digital Object Identifier: 10.1214/aos/1176348768

Primary: 62G05
Secondary: 62G20

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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