IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v74y2005i1p59-66.html
   My bibliography  Save this article

On almost sure limit theorems for positively dependent random variables

Author

Listed:
  • Matula, Przemyslaw

Abstract

In this note, we prove an almost sure limit theorem for pairwise quadrant-dependent random variables. From the main result, we obtain the Glivenko-Cantelli lemma for pairwise PQD and the almost sure central limit theorem for i.i.d. random variables.

Suggested Citation

  • Matula, Przemyslaw, 2005. "On almost sure limit theorems for positively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 59-66, August.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:1:p:59-66
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00159-8
    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. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    2. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. H. Jabbari, 2013. "On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables," Statistical Papers, Springer, vol. 54(3), pages 765-772, August.

    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. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    2. Luísa Pereira & Zhongquan Tan, 2017. "Almost Sure Convergence for the Maximum of Nonstationary Random Fields," Journal of Theoretical Probability, Springer, vol. 30(3), pages 996-1013, September.
    3. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    4. H. Jabbari, 2013. "On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables," Statistical Papers, Springer, vol. 54(3), pages 765-772, August.
    5. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
    6. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
    7. Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
    8. Horvath, Lajos & Khoshnevisan, Davar, 1995. "Weight functions and pathwise local central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 105-123, September.
    9. István Fazekas & Alexey Chuprunov, 2007. "An Almost Sure Functional Limit Theorem for the Domain of Geometric Partial Attraction of Semistable Laws," Journal of Theoretical Probability, Springer, vol. 20(2), pages 339-353, June.
    10. Chen, Pingyan & Sung, Soo Hak, 2016. "A strong law of large numbers for nonnegative random variables and applications," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 80-86.
    11. Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.
    12. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
    13. Miao, Yu & Wang, Rujun & Adler, Andre, 2016. "Limit theorems for order statistics from exponentials," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 51-57.
    14. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    15. István Berkes & Siegfried Hörmann & Lajos Horváth, 2010. "On Functional Versions of the Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 23(1), pages 109-126, March.
    16. Csáki, E. & Földes, A., 1995. "On the logarithmic average of additive functionals," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 261-268, March.
    17. Bercu, Bernard & Nourdin, Ivan & Taqqu, Murad S., 2010. "Almost sure central limit theorems on the Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1607-1628, August.
    18. Etemadi, N., 2007. "Stability of weighted averages of 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 389-395, February.
    19. Tabacu, Lucia & Ledbetter, Mark, 2019. "Change-point analysis using logarithmic quantile estimation," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 94-100.
    20. Xu, Feng & Wu, Qunying, 2017. "Almost sure central limit theorem for self-normalized partial sums of ρ−-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 17-27.

    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:74:y:2005:i:1:p:59-66. 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.