IDEAS home Printed from
   My bibliography  Save this article

On conditional distributions of nearest neighbors


  • Kaufmann, E.
  • Reiss, R. -D.


Let X1, ..., Xn be i.i.d. S-valued random variables and let g be a real-valued function on S. We give an explicit representation of the conditional distribution of the empirical point process based on X1, ..., Xn given the (k + 1)th smallest order statistic of the r.v.'s g(X1), ..., g(Xn). The extension to conditioning on several of the order statistics of g(X1), ..., g(Xn) is indicated. The result for point processes enables us to deduce the conditional distribution of the k smallest g-order statistics taken in the order of their magnitude as well as in the order of their outcome. The latter r.v.'s are conditionally independent.

Suggested Citation

  • Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
  • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:67-76

    Download full text from publisher

    File URL:
    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.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    2. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jos Mara, 2009. "Multivariate order statistics via multivariate concomitants," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 946-951, May.
    3. Wang, Ke & Nagaraja, H.N., 2010. "Distribution of extremal order statistics from large subsets of concomitants," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 534-539, April.
    4. Díaz, Mateo & Quiroz, Adolfo J. & Velasco, Mauricio, 2019. "Local angles and dimension estimation from data on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 229-247.
    5. Qinying He & H. Nagaraja & Chunjie Wu, 2013. "Efficient simulation of complete and censored samples from common bivariate exponential distributions," Computational Statistics, Springer, vol. 28(6), pages 2479-2494, December.


    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:42:y:1992:i:1:p:67-76. 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: .

    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.