IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v2y1972i4p345-361.html
   My bibliography  Save this article

Weak convergence and relative compactness of martingale processes with applications to some nonparametric statistics

Author

Listed:
  • Sen, Pranab Kumar

Abstract

For forward and reverse martingale processes, weak convergence to appropriate stochastic (but, not necessarily, Wiener) processes is studied. In particular, it is shown that martingale processes are tight under a uniformly integrability condition, and also, convergence of finite dimensional distributions satisfying certain mild conditions implies the compactness of such processes. The theory is illustrated with the aid of a class of U-statistics and von Mises' differentiable statistical functions which need not be stationary of order zero. Weak convergence of the classical Cramér-von Mises goodness-of-fit statistic is also considered. The case of martingales with random indices is studied at the end.

Suggested Citation

  • Sen, Pranab Kumar, 1972. "Weak convergence and relative compactness of martingale processes with applications to some nonparametric statistics," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 345-361, December.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:4:p:345-361
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(72)90032-2
    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.

    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:jmvana:v:2:y:1972:i:4:p:345-361. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.