IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v90y2004i2p257-268.html
   My bibliography  Save this article

Covariance kernel and the central limit theorem in the total variation distance

Author

Listed:
  • Mikami, Toshio

Abstract

We modify and generalize the idea of covariance kernels for Borel probability measures on Rd, and study the relation between the central limit theorem in the total variation distance and the convergence of covariance kernels.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:90:y:2004:i:2:p:257-268
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00143-X
    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. Papadatos, N. & Papathanasiou, V., 1998. "Variational Inequalities for Arbitrary Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 154-168, November.
    2. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
    3. Mikami, Toshio, 1998. "Equivalent conditions on the central limit theorem for a sequence of probability measures on R," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 237-242, March.
    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. Papathanasiou, V., 1996. "Multivariate Variational Inequalities and the Central Limit Theorem," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 189-196, August.
    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. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.

    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. Papadatos, N. & Papathanasiou, V., 1998. "Variational Inequalities for Arbitrary Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 154-168, November.
    3. Mikami, Toshio, 1998. "Equivalent conditions on the central limit theorem for a sequence of probability measures on R," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 237-242, March.
    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. Landsman, Zinoviy & Vanduffel, Steven & Yao, Jing, 2015. "Some Stein-type inequalities for multivariate elliptical distributions and applications," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 54-62.
    6. Papadatos, N. & Papathanasiou, V., 1996. "A generalization of variance bounds," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 191-194, June.
    7. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.
    8. Arras, Benjamin & Azmoodeh, Ehsan & Poly, Guillaume & Swan, Yvik, 2019. "A bound on the Wasserstein-2 distance between linear combinations of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2341-2375.
    9. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    10. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    11. 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.
    12. Bobkov, S. G. & Houdré, C., 1997. "Converse Poincaré-type inequalities for convex functions," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 37-42, May.
    13. Arakelian, V. & Papathanasiou, V., 2004. "On bounding the absolute mean value," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 447-450, October.
    14. Christophe Ley & Gesine Reinert & Yvik Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.

    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:90:y:2004:i:2:p:257-268. 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.