IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v55y2001i2p181-186.html
   My bibliography  Save this article

An extension of the Erdös-Neveu-Rényi theorem with applications to order statistics

Author

Listed:
  • Kaluszka, M.
  • Okolewski, A.

Abstract

The necessary and sufficient conditions are given for some stochastic process to be an empirical distribution function from some exchangeable random variables. The result is applied to establish sharp lower and upper bounds for order statistics based on possibly dependent random variables.

Suggested Citation

  • Kaluszka, M. & Okolewski, A., 2001. "An extension of the Erdös-Neveu-Rényi theorem with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 181-186, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:181-186
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(01)00114-6
    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. Rychlik, Tomasz, 1992. "Stochastically extremal distributions of order statistics for dependent samples," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 337-341, April.
    2. Masaaki Sibuya, 1991. "Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 261-285, June.
    3. Rychlik, Tomasz, 1995. "Bounds for order statistics based on dependent variables with given nonidentical distributions," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 351-358, June.
    4. Caraux, G. & Gascuel, O., 1992. "Bounds on distribution functions of order statistics for dependent variates," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 103-105, May.
    5. Gascuel, O. & Caraux, G., 1992. "Bounds on expectations of order statistics via extremal dependences," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 143-148, September.
    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. Okolewski, Andrzej, 2017. "Extremal properties of order statistic distributions for dependent samples with partially known multidimensional marginals," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 1-9.
    2. Kaluszka, Marek & Okolewski, Andrzej, 2011. "Stability of L-statistics from weakly dependent observations," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 618-625, May.

    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. Papadatos, Nickos, 2001. "Distribution and expectation bounds on order statistics from possibly dependent variates," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 21-31, August.
    2. Tomasz Rychlik, 2001. "Stability of Order Statistics under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 877-894, December.
    3. Jing Cao & Ann Moosman & Valen E. Johnson, 2010. "A Bayesian Chi-Squared Goodness-of-Fit Test for Censored Data Models," Biometrics, The International Biometric Society, vol. 66(2), pages 426-434, June.
    4. Rychlik, Tomasz, 1995. "Bounds for order statistics based on dependent variables with given nonidentical distributions," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 351-358, June.
    5. Okolewski, Andrzej, 2017. "Extremal properties of order statistic distributions for dependent samples with partially known multidimensional marginals," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 1-9.
    6. Ying Yuan & Valen E. Johnson, 2012. "Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models," Biometrics, The International Biometric Society, vol. 68(1), pages 156-164, March.
    7. Chang Xuan Mao & Sining Chen & Yitong Yang, 2016. "A Population-Size Model for Protein Spot Detection in Proteomic Studies," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 170-180, March.
    8. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    9. Frolov, Andrei N., 2021. "On upper and lower bounds for probabilities of combinations of events," Statistics & Probability Letters, Elsevier, vol. 173(C).
    10. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    11. D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.
    12. Escudero, Laureano F. & Ortega, Eva-María, 2008. "Actuarial comparisons for aggregate claims with randomly right-truncated claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 255-262, October.
    13. Navarro, Jorge & Ruiz, Jose M. & Sandoval, Carlos J., 2005. "A note on comparisons among coherent systems with dependent components using signatures," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 179-185, April.

    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:55:y:2001:i:2:p:181-186. 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.