IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v56y2002i2p113-120.html
   My bibliography  Save this article

A uniform limit theorem for predictive distributions

Author

Listed:
  • Berti, Patrizia
  • Rigo, Pietro

Abstract

Let be a filtration, {Xn} an adapted sequence of real random variables, and {[alpha]n} a predictable sequence of non-negative random variables with [alpha]1>0. Set and define the random distribution functions and . Under mild assumptions on {[alpha]n}, it is shown that , a.s. on the set {Fn or Bn convergesuniformly}. Moreover, conditions are given under which Fn converges uniformly with probability 1.

Suggested Citation

  • Berti, Patrizia & Rigo, Pietro, 2002. "A uniform limit theorem for predictive distributions," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 113-120, January.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:113-120
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(01)00089-X
    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. Berti, Patrizia & Rigo, Pietro, 1997. "A Glivenko-Cantelli theorem for exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 385-391, April.
    2. Hanson, D. L. & Li, Gang, 1997. "A note on the empirical distribution of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 337-340, June.
    3. 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. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Limit Theorems for Empirical Processes Based on Dependent Data," Quaderni di Dipartimento 132, University of Pavia, Department of Economics and Quantitative Methods.
    2. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2024. "Hierarchical false discovery rate control for high-dimensional survival analysis with interactions," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    3. Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2009. "Rate of Convergence of Predictive Distributions for Dependent Data," Quaderni di Dipartimento 091, University of Pavia, Department of Economics and Quantitative Methods.

    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. 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.
    2. Matula, Przemyslaw, 2005. "On almost sure limit theorems for positively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 59-66, August.
    3. 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.
    4. Etemadi, N., 2007. "Stability of weighted averages of 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 389-395, February.
    5. Hashorva, Enkelejd, 2001. "Asymptotic results for FGM random sequences," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 417-425, October.
    6. Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    7. Alonso Ruiz, Patricia & Rakitko, Alexander, 2016. "The limit theorem for maximum of partial sums of exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 357-362.

    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:56:y:2002:i:2:p:113-120. 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.