IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v48y2000i2p105-119.html
   My bibliography  Save this article

Explicit bounds on Lévy-Prohorov distance for a class of multidimensional distribution functions

Author

Listed:
  • Dewan, Isha
  • Rao, B. L. S. Prakasa

Abstract

Let F(x1,...,xk) and G(x1,...,xk)=FX1(x1)...FXk(xk), where FXi(xi), 1[less-than-or-equals, slant]i[less-than-or-equals, slant]k, are the one-dimensional marginal distributions of F, be two distribution functions on . Here, we obtain explicit bounds for the Lévy-Prohorov distance between F and G using some general results due to Yurinskii (1975, Theory Probab. Appl. 20, 1-10).

Suggested Citation

  • Dewan, Isha & Rao, B. L. S. Prakasa, 2000. "Explicit bounds on Lévy-Prohorov distance for a class of multidimensional distribution functions," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 105-119, June.
  • Handle: RePEc:eee:stapro:v:48:y:2000:i:2:p:105-119
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00179-0
    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. Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
    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. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    2. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    3. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    4. Chaubey, Yogendra P. & Dewan, Isha & Li, Jun, 2011. "Smooth estimation of survival and density functions for a stationary associated process using Poisson weights," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 267-276, February.
    5. Garg, Mansi & Dewan, Isha, 2015. "On asymptotic behavior of U-statistics for associated random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 209-220.
    6. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    7. Isha Bagai & B. Prakasa Rao, 1995. "Kernel-type density and failure rate estimation for associated sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 253-266, June.
    8. Li, Yongming & Yang, Shanchao & Wei, Chengdong, 2011. "Some inequalities for strong mixing random variables with applications to density estimation," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 250-258, February.
    9. Dewan, Isha & Rao, B.L.S. Prakasa, 2005. "Wilcoxon-signed rank test for associated sequences," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 131-142, February.
    10. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    11. Isha Dewan & B. Rao, 1997. "Remarks on the strong law of large numbers for a triangular array of associated random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 225-234, January.
    12. Isha Dewan & B. Rao, 2003. "Mann-Whitney test for associated sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 111-119, March.
    13. Roussas, George G., 2001. "An Esséen-type inequality for probability density functions, with an application," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 397-408, February.
    14. Dudzinski, Marcin, 2008. "The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 347-357, March.
    15. Yogendra P. Chaubey & Isha Dewan & Jun Li, 2021. "On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 114-139, May.

    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:48:y:2000:i:2:p:105-119. 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.