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Variational Inequalities for Arbitrary Multivariate Distributions

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. Papathanasiou, V., 1996. "Multivariate Variational Inequalities and the Central Limit Theorem," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 189-196, August.
    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.
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    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.

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