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Almost sure invariance principles for mixing sequences of random variables

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  • Shao, Qi-Man

Abstract

An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies [Sigma]nø(2n) 1. A similar result is also given under a higher moment condition.

Suggested Citation

  • Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:2:p:319-334
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    Citations

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    Cited by:

    1. Xuejun Wang & Meimei Ge & Yi Wu, 2019. "The asymptotic properties of the estimators in a semiparametric regression model," Statistical Papers, Springer, vol. 60(6), pages 2087-2108, December.
    2. Chen, Pingyan & Gan, Shixin, 2008. "On moments of the maximum of normed partial sums of [rho] -mixing random variables," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1215-1221, August.
    3. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    4. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    5. Florence Merlevède & Magda Peligrad, 2006. "On the Weak Invariance Principle for Stationary Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 19(3), pages 647-689, December.
    6. Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.
    7. Bashtova, Elena & Shashkin, Alexey, 2022. "Strong Gaussian approximation for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1-18.
    8. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    9. Su, Zhonggen, 2005. "The law of the iterated logarithm for character ratios," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 337-346, March.
    10. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    11. Christophe Cuny & Florence Merlevède, 2015. "Strong Invariance Principles with Rate for “Reverse” Martingale Differences and Applications," Journal of Theoretical Probability, Springer, vol. 28(1), pages 137-183, March.
    12. Hafouta, Yeor, 2023. "An almost sure invariance principle for some classes of non-stationary mixing sequences," Statistics & Probability Letters, Elsevier, vol. 193(C).
    13. Zhang, Li-Xin, 1996. "Complete convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 165-170, October.
    14. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "Complete moment convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 839-846, May.
    15. Liu, Weidong & Lin, Zhengyan, 2009. "Strong approximation for a class of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 249-280, January.

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