IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i12p1808-1812.html
   My bibliography  Save this article

A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices

Author

Listed:
  • Chen, Pingyan
  • Hao, Chunyan

Abstract

In this work, a sharp upper bound on the law of the logarithm for the weighted sums of random variables with multidimensional indices is obtained. The main result improves the result in [Li, Rao and Wang, 1995. On strong law of large numbers and the law of the logarithm for weighted sums of independent random variables with multidimensional indices. J. Multivariate Anal. 52, 181–198], partly.

Suggested Citation

  • Chen, Pingyan & Hao, Chunyan, 2011. "A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1808-1812.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1808-1812
    DOI: 10.1016/j.spl.2011.07.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002380
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2011.07.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Li, D. L. & Rao, M. B. & Wang, X. C., 1995. "On the Strong Law of Large Numbers and the Law of the Logarithm for Weighted Sums of Independent Random Variables with Multidimensional Indices," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 181-198, February.
    2. Kaffes, D. & Bhaskara Rao, M., 1982. "Weak consistency of least-squares estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 186-198, June.
    3. Gu, Wentao & Roussas, George G. & Tran, Lanh T., 2007. "On the convergence rate of fixed design regression estimators for negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1214-1224, July.
    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. Ko, Mi-Hwa, 2013. "On complete convergence for weighted sums of asymptotically linear negatively dependent random field," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2615-2620.
    2. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    3. Li, Deli & Bhaskara Rao, M. & Tomkins, R. J., 2001. "The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 191-217, August.
    4. 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.
    5. Sung, Soo Hak, 2009. "A law of the single logarithm for weighted sums of i.i.d. random elements," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1351-1357, May.
    6. D. Li & R. J. Tomkins, 2003. "The Law of the Logarithm for Weighted Sums of Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(3), pages 519-542, July.
    7. Li, Deli, 1996. "Bounded and compact laws of the logarithm for B-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 189-209, November.
    8. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    9. Feng, Xinwei, 2019. "Law of the logarithm for weighted sums of negatively dependent random variables under sublinear expectation," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 132-141.

    More about this item

    Keywords

    Law of the logarithm; Weighted sum;

    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:81:y:2011:i:12:p:1808-1812. 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.