Estimation of variance of partial sums of an associated sequence of random variables

Let Xn, n ⩾ 1 be a stationary sequence of associated random variables satisfying E(X1) = μ, E(X21) < ∞ and (Var Sn)n → σ2 as n → ∞. In this paper, an estimator of σ2 based on the subseries values using overlapping blocks is studied. A central limit theorem related to this estimator is obtained.