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

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.