A weak convergence result for sequential empirical processes under weak dependence

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying alpha-mixing triangular array of random variables. In particular, the uniformly boundedness assumption on the function class, which is required in most of the existing literature, is spared. Furthermore, under strict stationarity a weak convergence result for the sequential empirical process indexed in function classes is obtained as a direct consequence. Two examples in mathematical statistics, that cannot be treated with existing results, are given as possible applications.