Empirical Distribution Function for m(n)-dependent Sample and Its Application to Hazard’s Estimate

Let X be a random variable and X_n a sequence of realizations of X which are not necessarily assumed to be independent. We derive a generalization of of Glivenko-Cantelli theorem and the uniform rate of convergence on a compact set of density kernel estimate under the condition that X_n is a m(n)-dependent sequence. These results together lead to uniform rate of convergence of hazard kernel estimate.