The weighted empirical process of row independent random variables with arbitrary distribution functions

The relative compactness and weak convergence of reduced empirical, quantile and weighted empirical processes are demonstrated under mild conditions. For example, the reduced empirical proces of arbitrary independent iv'S is always relatively compact in any ‖/q‖ metric with q square integrable; and weak convergence takes place if and only if the covariance function converges. Van Zuijlen's representation of the general empirical process is a fundamental tool. This paper both unifies and extends the previous treatment of these processes ‐ processes that have application to rank statistics and linear combinations of order statistics. Most proofs are contained in Section 3. A brief introduction to weak convergence is presented in the appendix for readers lacking this background. Applications are indicated in Section 4.