Uniform convergence of an empirical cdf based on a relatively small number of order statistics
Joel Edmund Michalek · Communication in Statistics- Theory and Methods · 1976
An empirical distribution function Fm, defined on a subset of order statistics of a random sample of size n taken from the distribution of a random variable with continuous distribution function F, is shown to converge uniformly with probability one to F. Small sample distributions of the one and two sided deviations and the asymptotic normality of the standardized Fm are established. The relative efficiency of Fm as compared to the classical empirical distribution function is calculated and tabled. for n = 10, 20, 50, 100, 200.