ON THE CONVERGENCE OF EMPIRICAL PROCESSES OF MIXING VARIABLES1

Abstract

Conditions are given for the weak convergence of (t—t2)LN(aN‐1(t)) to a Gaussian process where v<1/2, aN is a cdf and LN is the normalized weighted empirical cumulative distribution function (cdf) for an α‐mixing sample of random variables in R which may be non‐stationary with discontinuous marginals.