The Annals of Probability

A Law of the Logarithm for Kernel Density Estimators

Winfried Stute

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Abstract

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.

Article information

Source
Ann. Probab., Volume 10, Number 2 (1982), 414-422.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993866

Digital Object Identifier
doi:10.1214/aop/1176993866

Mathematical Reviews number (MathSciNet)
MR647513

Zentralblatt MATH identifier
0493.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F15: Strong theorems 62E20: Asymptotic distribution theory

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

Citation

Stute, Winfried. A Law of the Logarithm for Kernel Density Estimators. Ann. Probab. 10 (1982), no. 2, 414--422. doi:10.1214/aop/1176993866. https://projecteuclid.org/euclid.aop/1176993866


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