IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v67y1998i2p154-168.html
   My bibliography  Save this article

Variational Inequalities for Arbitrary Multivariate Distributions

Author

Listed:
  • Papadatos, N.
  • Papathanasiou, V.

Abstract

Upper bounds for the total variation distance between two arbitrary multivariate distributions are obtained in terms of the correspondingw-functions. The results extend some previous inequalities satisfied by the normal distribution. Some examples are also given.

Suggested Citation

  • Papadatos, N. & Papathanasiou, V., 1998. "Variational Inequalities for Arbitrary Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 154-168, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:154-168
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91758-4
    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. Papathanasiou, V., 1993. "Some Characteristic Properties of the Fisher Information Matrix via Cacoullos-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 256-265, February.
    2. Chen, Louis H. Y., 1982. "An inequality for the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 306-315, June.
    3. Papathanasiou, V., 1996. "Multivariate Variational Inequalities and the Central Limit Theorem," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 189-196, August.
    4. Cacoullos, T. & Papathanasiou, V., 1992. "Lower variance bounds and a new proof of the central limit theorem," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 173-184, November.
    5. Chou, Jine-Phone, 1988. "An identity for multidimensional continuous exponential families and its applications," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 129-142, January.
    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. Mikami, Toshio, 2004. "Covariance kernel and the central limit theorem in the total variation distance," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 257-268, August.
    2. Giorgos Afendras & Vassilis Papathanasiou, 2014. "A note on a variance bound for the multinomial and the negative multinomial distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 179-183, April.

    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. Giorgos Afendras & Vassilis Papathanasiou, 2014. "A note on a variance bound for the multinomial and the negative multinomial distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 179-183, April.
    2. Mikami, Toshio, 2004. "Covariance kernel and the central limit theorem in the total variation distance," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 257-268, August.
    3. Wei, Zhengyuan & Zhang, Xinsheng, 2008. "A matrix version of Chernoff inequality," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1823-1825, September.
    4. N. Nair & K. Sudheesh, 2008. "Some results on lower variance bounds useful in reliability modeling and estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 591-603, September.
    5. Takis Papaioannou & Kosmas Ferentinos & Charalampos Tsairidis, 2007. "Some Information Theoretic Ideas Useful in Statistical Inference," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 307-323, June.
    6. Tang, Hsiu-Khuern & See, Chuen-Teck, 2009. "Variance inequalities using first derivatives," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1277-1281, May.
    7. Barman, Kalyan & Upadhye, Neelesh S., 2022. "On Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution," Statistics & Probability Letters, Elsevier, vol. 189(C).
    8. Gibilisco, Paolo & Imparato, Daniele & Isola, Tommaso, 2008. "Stam inequality on," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1851-1856, September.
    9. R. Korwar, 1991. "On characterizations of distributions by mean absolute deviation and variance bounds," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 287-295, June.
    10. Hornik, Kurt & Grün, Bettina, 2014. "On standard conjugate families for natural exponential families with bounded natural parameter space," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 14-24.
    11. Nair, N. Unnikrishnan & Sankaran, P.G., 2008. "Characterizations of multivariate life distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2096-2107, October.
    12. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    13. Mohtashami Borzadaran, G. R. & Shanbhag, D. N., 1998. "Further results based on Chernoff-type inequalities," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 109-117, August.
    14. Bobkov, S. G. & Houdré, C., 1997. "Converse Poincaré-type inequalities for convex functions," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 37-42, May.
    15. Wei, Zhengyuan & Zhang, Xinsheng, 2009. "Covariance matrix inequalities for functions of Beta random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 873-879, April.
    16. Giorgos Afendras, 2013. "Unified extension of variance bounds for integrated Pearson family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 687-702, August.
    17. Pommeret Denys, 2002. "Information Inequalities For The Risks In Simple Quadratic Exponential Families," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 81-94, April.
    18. Goodarzi, F. & Amini, M. & Mohtashami Borzadaran, G.R., 2016. "On upper bounds for the variance of functions of the inactivity time," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 62-71.

    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:67:y:1998:i:2:p:154-168. 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.