IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i10p1215-1221.html
   My bibliography  Save this article

On moments of the maximum of normed partial sums of [rho] -mixing random variables

Author

Listed:
  • Chen, Pingyan
  • Gan, Shixin

Abstract

Let {Xn,n>=1} be a sequence of identically distributed [rho]-mixing random variables and set . Under suitable mixing rate restriction, the sufficient and necessary conditions for the existence of the moments of supn>=1Sn/n1/rp(0 0) are given, which are same as that in the independent case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1215-1221
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00395-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    2. 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.
    3. Choi, Bong Dae & Sung, Soo Hak, 1987. "On moment conditions for the supremum of normed sums," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 99-106.
    4. Li, Deli & Huang, Mei Ling, 1998. "A note on moments of the maximum of Cesàro summation," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 73-81, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    3. Chen, Pingyan & Chen, Ran, 2010. "A remark on LSL for weighted sums of i.i.d random elements," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1329-1334, September.
    4. Bashtova, Elena & Shashkin, Alexey, 2022. "Strong Gaussian approximation for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1-18.
    5. Shuhe, Hu & Ming, Hu, 2006. "A general approach rate to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 843-851, April.
    6. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.
    7. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    8. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    9. Hafouta, Yeor, 2023. "An almost sure invariance principle for some classes of non-stationary mixing sequences," Statistics & Probability Letters, Elsevier, vol. 193(C).
    10. Boukhari, Fakhreddine, 2020. "The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 161(C).
    11. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    12. Zhang, Li-Xin, 1996. "Complete convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 165-170, October.
    13. 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.
    14. Li, Deli & Huang, Mei Ling, 1998. "A note on moments of the maximum of Cesàro summation," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 73-81, May.
    15. 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.
    16. 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.
    17. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    18. 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.
    19. 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.
    20. Su, Zhonggen, 2005. "The law of the iterated logarithm for character ratios," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 337-346, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1215-1221. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.