Consider a sequence of stationary, negatively associated random variables, and set , , and , with denoting the mean of , and a real function satisfying some conditions. The author’s main results provide an asymptotic Wiener process approximation for the partial sum process of the , both in the case of being a fixed positive integer as well as for , but as . A corresponding result for positively associated random variables is also presented.
As a consequence of the main results, the author is able to derive asymptotic normality of some estimators of the asymptotic variance of , which have earlier been discussed by M. Peligrad and Q.-M. Shao [ibid. 52, No. 1, 140-157 (1995; Zbl 0816.62027)] and M. Peligrad and R. Suresh [Stochastic Processes Appl. 56, No. 2, 307-319 (1995; Zbl 0817.62019)] in case of -mixing variables, and by Zhang and Shi (1998) for negatively associated variables.