IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-05261-3_4.html
   My bibliography  Save this book chapter

Estimates of the Difference of Two Distribution Functions

In: Probability Inequalities

Author

Listed:
  • Zhengyan Lin

    (Zhejiang University, Department of Mathematics)

  • Zhidong Bai

    (Northeast Normal University, School of Mathematics and Statistics
    National University of Singapore, Department of Statistics and Applied Probabilty)

Abstract

Rates of weak convergence are important for application of weak limit theorems. Thus, investigation on convergence rates has been an active research topic for decades. Generally speaking, the convergence rates are established by various basic inequalities between two distribution functions and/or functions of bounded variation in terms of various transformations. The first work was done be Berry-Esseen who established the convergence rate of normal approximation in terms of Fourier transformations or characteristic functions. Stein and Chen created a new method to evaluate the convergence rates of normal or Poisson approximation for non-independent sums. In 1993, Bai established convergence rates of empirical spectral distributions of large dimensional random matrices in terms of Stieltjes transforms. In this chapter, we only introduce some basic inequalities of difference of two distribution functions. Their applications can be found in (1995), (1986) and (1993).

Suggested Citation

  • Zhengyan Lin & Zhidong Bai, 2010. "Estimates of the Difference of Two Distribution Functions," Springer Books, in: Probability Inequalities, chapter 0, pages 29-36, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-05261-3_4
    DOI: 10.1007/978-3-642-05261-3_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-642-05261-3_4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.