STRONG APPROXIMATION OF RANDOM WEIGHTING METHODS AND ITS APPLICATION

In this paper, we get the rate of strong approximation of Random Weighting Methods on the empirical process and the quantile process, i.e. under some conditions, we have, \begingathered\sup _-\inftyα_n（x）, Q_n^*（t）, B_n（x）and n^-1/2K（t, n） are the empirical process, the quantile process, Brownian bridge and Kiefer process respectively.