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

Shan Sun and Ching-Yuan Chiang

International Journal of Stochastic Analysis, 1997, vol. 10, 1-18


We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic F ˆ n ( U n ) for a class of strongly mixing sequences of random variables { X i , i ≥ 1 } . Stationarity is not assumed. Here F ˆ n is the perturbed empirical distribution function and U n is a U -statistic based on X 1 , … , X n .

Date: 1997
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DOI: 10.1155/S1048953397000026

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