A Law of the Logarithm for Kernel Density Estimators

Winfried Stute

doi:10.1214/aop/1176993866

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Home > Journals > Ann. Probab. > Volume 10 > Issue 2 > Article

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

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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.

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