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

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  • 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
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    References listed on IDEAS

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    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. Papathanasiou, V., 1996. "Multivariate Variational Inequalities and the Central Limit Theorem," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 189-196, August.
    3. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
    4. 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.
    5. 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.
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    Cited by:

    1. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.

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