Estimation of the Variance of Partial Sums for ρ-Mixing Random Variables

Let {Xn, n ≥ 1} be a stationary sequence of ρ-mixing random variables satisfying EXn = μ, EX2n < ∞, Var Sn/n → σ2 > 0. This paper presents a class of estimators of σ 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.