The weak convergence for functions of negatively associated random variables

Let {X-n, n greater than or equal to 1} be a sequence of stationary negativ ely associated random variables, S-j(l) = Sigma (l)(i = 1) Xj + i, S-n = Si gma (n)(i = l) X-i. Suppose that f(x) is a real function. Under some suitab le conditions, the central limit theorem and the weak convergence for sums Sigma (n)(j=l) f(Sj(l)/rootl), n greater than or equal to 1. are investigated. Applications to limiting distributions of estimators of V ar S-n are also discussed. (C) 2001 Academic Press.