Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

cc-by We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic F̂n(Un) for a class of strongly mixing sequences of random variables {Xi,i ≥ 1}. Stationarity is not assumed. Here F̂n is the perturbed empirical distribution function and Un...

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Bibliographic Details
Published in:Journal of Applied Mathematics and Stochastic Analysis
Main Authors: Sun, Shan (TTU), Chiang, Ching Yuan
Format: Article in Journal/Newspaper
Language:English
Published: 1997
Subjects:
Almost Sure Representation
Invariance Principle
Law of the Iterated Logarithm
Perturbed Empirical Distribution Functions
Strong Mixing
U-statistic
North Atlantic
Online Access:https://hdl.handle.net/2346/95704
https://doi.org/10.1155/S1048953397000026
Description
Summary:cc-by We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic F̂n(Un) for a class of strongly mixing sequences of random variables {Xi,i ≥ 1}. Stationarity is not assumed. Here F̂n is the perturbed empirical distribution function and Un is a U-statistic based on X1,., Xn. ©1997 by North Atlantic Science Publishing Company.

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