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Asymptotics for multivariate t-statistic for random vectors in the generalized domain of attraction of the multivariate normal law

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  • Sepanski, Steven J.

Abstract

We define the appropriate analogue of Student's t-statistic for multivariate data, and prove that it is asymptotically normal for random vectors in the Generalized Domain of Attraction of the Normal Law. This extends an earlier result where asymptotic normality was proved under the stronger hypothesis of Domain of Attraction.

Suggested Citation

  • Sepanski, Steven J., 1996. "Asymptotics for multivariate t-statistic for random vectors in the generalized domain of attraction of the multivariate normal law," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 179-188, October.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:2:p:179-188
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    References listed on IDEAS

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    1. Maller, R. A., 1993. "Quadratic Negligibility and the Asymptotic Normality of Operator Normed Sums," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 191-219, February.
    2. Sepanski, Steven J., 1994. "Necessary and sufficient conditions for the multivariate bootstrap of the mean," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 205-216, February.
    3. Sepanski, S. J., 1994. "Asymptotics for Multivariate t-Statistic and Hotelling's T2-Statistic Under Infinite Second Moments via Bootstrapping," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 41-54, April.
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    Cited by:

    1. Martsynyuk, Yuliya V., 2013. "On the generalized domain of attraction of the multivariate normal law and asymptotic normality of the multivariate Student t-statistic," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 402-411.
    2. Lu, Zeng-Hua, 2013. "Halfline tests for multivariate one-sided alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 479-490.
    3. Martsynyuk, Yuliya V., 2012. "Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2270-2277.
    4. Steven J. Sepanski, 1997. "Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law," Journal of Theoretical Probability, Springer, vol. 10(4), pages 1053-1063, October.

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