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Bootstrapping the sample means for stationary mixing sequences


  • Shao, Qi-Man
  • Yu, Hao


We propose a circular block resampling procedure to modify Künsch's moving block bootstrap. Our procedure has the special feature that the resampled data are like drawing from the empirical distribution function of dependent observations. No information is lost concerning the nature of dependency of the original observations coming from a general stationary sequence. We prove two general theorems on bootstrapping sample means for stationary sequences. Applications to stationary [alpha]-mixing, [rho]-mixing and [phi]-mixing sequences are also discussed.

Suggested Citation

  • Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
  • Handle: RePEc:eee:spapps:v:48:y:1993:i:1:p:175-190

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    Cited by:

    1. Andrés Alonso & Daniel Peña & Juan Romo, 2003. "Resampling time series using missing values techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 765-796, December.
    2. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    3. Psaradakis, Zacharias, 2001. "On bootstrap inference in cointegrating regressions," Economics Letters, Elsevier, vol. 72(1), pages 1-10, July.
    4. Dehling, Herold & Wendler, Martin, 2010. "Central limit theorem and the bootstrap for U-statistics of strongly mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 126-137, January.
    5. 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.
    6. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2000. "Resampling time series by missing values techniques," DES - Working Papers. Statistics and Econometrics. WS 9923, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Dehling, Herold & Sharipov, Olimjon Sh. & Wendler, Martin, 2015. "Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 200-215.
    8. Hwang, Eunju & Shin, Dong Wan, 2012. "Strong consistency of the stationary bootstrap under ψ-weak dependence," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 488-495.
    9. Csörgo, Miklós & Yu, Hao, 1997. "Estimation of total time on test transforms for stationary observations," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 229-253, June.
    10. Zacharias Psaradakis, 2008. "Assessing Time-Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
    11. Sharipov, Olimjon Sh. & Wendler, Martin, 2013. "Normal limits, nonnormal limits, and the bootstrap for quantiles of dependent data," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1028-1035.


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