Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables. (1997) - Sun, Shan; Chiang, Ching-Yuan
Abstract : 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 .