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

Shan Sun, Ching-Yuan Chiang
1997 Journal of Applied Mathematics and Stochastic Analysis  
We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statisticFˆn(Un)for a class of strongly mixing sequences of random variables{Xi,i≥1}. Stationarity is not assumed. HereFˆnis the perturbed empirical distribution function andUnis aU-statistic based onX1,...,Xn.
doi:10.1155/s1048953397000026 fatcat:yony2aqvknevpoa7kk6zfarwc4