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Equivalent conditions on the central limit theorem for a sequence of probability measures on R

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  • Mikami, Toshio

Abstract

In this paper we give equivalent conditions on the central limit theorem in total variation norm for a sequence of probability measures on R. This generalizes Cacoullos, Papathanasiou and Utev's central limit theorem in L1-norm for a sequence of probability density functions on R. We also give equivalent conditions on the central limit theorem in weak convergence and those on the local limit theorem.

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  • 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.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:3:p:237-242
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    References listed on IDEAS

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    1. Cacoullos, T. & Papathanasiou, V., 1989. "Characterizations of distributions by variance bounds," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 351-356, April.
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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. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.

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