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

ShanSun; Ching-YuanChiang

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

机译：对于随机变量的强烈混合序列，在U统计量下评估的扰动经验分布函数的极限行为

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摘要

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statisticF?n(Un)for a class of strongly mixing sequences of random variables{Xi,i≥1}. Stationarity is not assumed. HereF?nis the perturbed empirical distribution function andUnis aU-statistic based onX1,…,Xn.

机译：我们证明了一类强混合随机变量{Xi，i≥1}的类的统计量F？n（Un）的几乎确定的表示形式，对数的定律和不变性原理。不假定平稳性。这里，Fs是受扰动的经验分布函数和基于X1，…，Xn的Unis aU统计量。

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《International journal of stochastic analysis》 |1997年第1期|共18页
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ShanSun; Ching-YuanChiang;
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中图分类应用数学;
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7. Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables [O] . Shan Sun, Ching-Yuan Chiang 1997

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8. Empirical Distribution Functions and Functions of Order Statistics for Mixing Random Variables [R] . Puri, M. L., Tran, L. T. 1979

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

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