Estimation of the Variance of Partial Sums for [rho]-Mixing Random Variables

Let {Xn, n >= 1} be a stationary sequence of [rho]-mixing random variables satisfying EXn = [mu], EX2n < [infinity], Var Sn/n --> [sigma]2 > 0. This paper presents a class of estimators of [sigma] and investigates their weak consistency as well as their asymptotic normality. Applications to the self-normalizing central limit theorem and confidence for the sample mean are also discussed.