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

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  • Peligrad, M.
  • Shao, Q. M.

Abstract

Let {Xn, n >= 1} be a stationary sequence of [rho]-mixing random variables satisfying EXn = [mu], EX2n [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.

Suggested Citation

  • Peligrad, M. & Shao, Q. M., 1995. "Estimation of the Variance of Partial Sums for [rho]-Mixing Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 140-157, January.
    • Handle: RePEc:eee:jmvana:v:52:y:1995:i:1:p:140-157
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    Cited by:

    1. Dehling, Herold & Fried, Roland & Sharipov, Olimjon Sh. & Vogel, Daniel & Wornowizki, Max, 2013. "Estimation of the variance of partial sums of dependent processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 141-147.
    2. Jiang, Xinxin & Hahn, Marjorie, 2008. "A self-normalized central limit theorem for [rho] -mixing stationary sequences," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1541-1547, September.
    3. Zhang, Li-Xin, 2001. "The Weak Convergence for Functions of Negatively Associated Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 272-298, August.
    4. Peligrad, Magda & Shao, Qi-Man, 1996. "A note on estimation of variance for [rho]-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 141-145, February.
    5. Dehling, Herold & Fried, Roland, 2012. "Asymptotic distribution of two-sample empirical U-quantiles with applications to robust tests for shifts in location," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 124-140.
    6. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.

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