A Law of the Logarithm for Kernel Density Estimators
Winfried Stute
Source: Ann. Probab. Volume 10, Number 2
(1982), 414-422.
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.
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Keywords: Empirical distribution function; kernel density estimator; oscillation modulus; higher derivatives; optimal window-widths
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1176993866
JSTOR: links.jstor.org
Digital Object Identifier: doi:10.1214/aop/1176993866
Mathematical Reviews number (MathSciNet): MR647513
Zentralblatt MATH identifier: 0493.62040
