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

[摘要] 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.

[学科分类] 应用数学