Some laws of the iterated logarithm for empirical processes rescaled in the "time" parameter are presented. These laws of the iterated logarithm are applied to obtain strong limit theorems for M-estimators. In particular, a law of the iterated logarithm for M-estimators with unusual rates of...

The law of the iterated logarithm for canonical or completely degenerate U-statistics with square integrable kernel h is proved, for h taking values in 1, 7 and, in general, in a type 2 separable Banach space. The LIL is also obtained for U-processes indexed by canonical Vapnik-Cervonenkis...

We give some easy methods to check sufficient conditions for the weak convergence of stochastic processes indexed by smooth functions. The main condition is a moment condition on the increments of the process. We apply this to empirical processes and U-processes in the independent identically...

We study the weak convergence for the row sums of a triangular array of empirical processes under bracketing conditions involving majorizing measures. As an application, we consider the weak convergence of stochastic processes of the form where {Xj}j=1[infinity] is a sequence of i.i.d.r.v.s with...

Exponential inequalities, the law of the iterated logarithm and the bootstrap central limit theorem for U-processes indexed by Vapnik-Cervonenkis classes of functions are derived. These results are then applied to the asymptotics and the bootstrap of U-statistics with estimated parameters, in...

Let {Xj}j=1[infinity] be a stationary Gaussian sequence of random vectors with mean zero. We study the convergence in distribution of an-1[summation operator]j=1n (G(Xj)-E[G(Xj)]), where G is a real function in with finite second moment and {an} is a sequence of real numbers converging to...