an:01023065
Zbl 0873.62050
Sun, Shan; Chiang, Ching-Yuan
Limiting behavior of the perturbed empirical distribution functions evaluated at \(U\)-statistics for strongly mixing sequences of random variables
EN
J. Appl. Math. Stochastic Anal. 10, No. 1, 3-20 (1997).
00038781
1997
j
62G20 62G30 60F17 60F15 62E20
almost sure representation; law of the iterated logarithm; invariance principle; strongly mixing sequences of random variables; perturbed empirical distribution function; \(U\)-statistic
Summary: We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic \(\widehat{F}_n(U_n)\) for a class of strongly mixing sequences of random variables \(\{X_i, i\geq 1\}\). Stationarity is not assumed. Here \(\widehat{F}_n\) is the perturbed empirical distribution function and \(U_n\) is a \(U\)-statistic based on \(X_1,\dots,X_n\).