Weak Convergence of Weighted Empirical U-Statistics Processes for Dependent Random Variables

A weak convergence of the weighted empirical U-statistic with respect to the Skorohod topology is obtained for absolutely regular random variables. It is a generalization of the results of F. H, Ruymgaart and M. C. A. van Zuijlen (1991, J. Statist. Plann. Inference) for i.i.d. random variables.