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May, 1982 A Law of the Logarithm for Kernel Density Estimators
Winfried Stute
Ann. Probab. 10(2): 414-422 (May, 1982). DOI: 10.1214/aop/1176993866


In this paper we derive a law of the logarithm for the maximal deviation between a kernel density estimator and the true underlying density function. Extensions to higher derivatives are included. The results are applied to get optimal window-widths with respect to almost sure uniform convergence.


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Winfried Stute. "A Law of the Logarithm for Kernel Density Estimators." Ann. Probab. 10 (2) 414 - 422, May, 1982.


Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0493.62040
MathSciNet: MR647513
Digital Object Identifier: 10.1214/aop/1176993866

Primary: 62G05
Secondary: 60F15 , 62E20

Keywords: Empirical distribution function , higher derivatives , kernel density estimator , optimal window-widths , oscillation modulus

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • May, 1982
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