IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v58y2002i3p297-307.html
   My bibliography  Save this article

Rates of uniform convergence of empirical means with mixing processes

Author

Listed:
  • Karandikar, Rajeeva L.
  • Vidyasagar, M.

Abstract

It has been shown previously by Nobel and Dembo (Stat. Probab. Lett. 17 (1993) 169) that, if a family of functions has the property that empirical means based on an i.i.d. process converge uniformly to their values as the number of samples approaches infinity, then continues to have the same property if the i.i.d. process is replaced by a [beta]-mixing process. In this note, this result is extended to the case where the underlying probability is itself not fixed, but varies over a family of measures. Further, explicit upper bounds are derived on the rate at which the empirical means converge to their true values, when the underlying process is [beta]-mixing. These bounds are less conservative than those derived by Yu (Ann. Probab. 22 (1994) 94).

Suggested Citation

  • Karandikar, Rajeeva L. & Vidyasagar, M., 2002. "Rates of uniform convergence of empirical means with mixing processes," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 297-307, July.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:3:p:297-307
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00124-4
    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. Nobel, Andrew & Dembo, Amir, 1993. "A note on uniform laws of averages for dependent processes," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 169-172, June.
    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. Taisuke Otsu & Myung Hwan Seo, 2014. "Asymptotics for maximum score method under general conditions," STICERD - Econometrics Paper Series 571, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Ghosh Debashis, 2012. "Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-21, July.
    3. Myung Hwan Seo & Taisuke Otsu, 2016. "Local M-estimation with discontinuous criterion for dependent and limited observations," STICERD - Econometrics Paper Series /589, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Nobel, Andrew, 1995. "A counterexample concerning uniform ergodic theorems for a class of functions," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 165-168, August.
    5. Magda Peligrad, 2001. "A Note on the Uniform Laws for Dependent Processes Via Coupling," Journal of Theoretical Probability, Springer, vol. 14(4), pages 979-988, October.
    6. repec:cep:stiecm:/2014/571 is not listed on IDEAS
    7. Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    8. Salim Bouzebda & Youssouf Souddi & Fethi Madani, 2024. "Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    9. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.

    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:58:y:2002:i:3:p:297-307. 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.