The Weak Convergence for Functions of Negatively Associated Random Variables

Let {Xn, n⩾1} be a sequence of stationary negatively associated random variables, Sj(l)=∑li=1 Xj+i, Sn=∑ni=1 Xi. Suppose that f(x) is a real function. Under some suitable conditions, the central limit theorem and the weak convergence for sums∑j=1n f Sj(l)l, n⩾1,are investigated. Applications to limiting distributions of estimators of Var Sn are also discussed.