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The Law of the Iterated Logarithm for L p -Norms of Kernel Estimators of Cumulative Distribution Functions

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  • Fuxia Cheng

    (Department of Mathematics, Illinois State University, Normal, IL 61790, USA)

Abstract

In this paper, we consider the strong convergence of L p -norms ( p ≥ 1 ) of a kernel estimator of a cumulative distribution function (CDF). Under some mild conditions, the law of the iterated logarithm (LIL) for the L p -norms of empirical processes is extended to the kernel estimator of the CDF.

Suggested Citation

  • Fuxia Cheng, 2024. "The Law of the Iterated Logarithm for L p -Norms of Kernel Estimators of Cumulative Distribution Functions," Mathematics, MDPI, vol. 12(7), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1063-:d:1368695
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    References listed on IDEAS

    as
    1. Fuxia Cheng, 2017. "Strong uniform consistency rates of kernel estimators of cumulative distribution functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6803-6807, July.
    2. Jiangyan Wang & Fuxia Cheng & Lijian Yang, 2013. "Smooth simultaneous confidence bands for cumulative distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 395-407, June.
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