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On the law of the logarithm for density estimators

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  • Hall, Peter

Abstract

It has been conjectured that the form of the so-called 'law of the logarithm' for kernel density estimators depends on tail properties of the kernel. We show that this is not the case, and extend work of other authors to uniform convergence when the supremum is taken over an unbounded interval and when the kernel has unbounded support.

Suggested Citation

  • Hall, Peter, 1990. "On the law of the logarithm for density estimators," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 237-240, March.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:3:p:237-240
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    Cited by:

    1. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.

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