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

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

In this paper, we consider the strong convergence of Lp-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 Lp-norms of empirical processes is extended to the kernel estimator of the CDF.

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Veröffentlicht in:Mathematics (Basel) 2024-04, Vol.12 (7), p.1063
1. Verfasser: Cheng, Fuxia
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Conflicts of interest
Distribution functions
empirical CDF
Inequality
kernel estimator
LIL
Logarithms
Lp-norm
Norms
Random variables
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Zusammenfassung:In this paper, we consider the strong convergence of Lp-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 Lp-norms of empirical processes is extended to the kernel estimator of the CDF.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12071063