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Asymptotics for Multivariate t-Statistic and Hotelling's T2-Statistic Under Infinite Second Moments via Bootstrapping

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  • Sepanski, S. 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 domain of attraction of the normal law. We also prove that Hotelling's T2-statistic has a chi-squared limiting distribution for random vectors in the generalized domain of attraction of the normal law. Our tool in proving these results is the bootstrap. We prove that the bootstrap version of the multivariate t-statistic is asymptotically normal when the parent distribution is in the generalized domain of attraction of the normal law.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:1:p:41-54
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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. Xu, Jin & Gupta, Arjun K., 2006. "Improved confidence regions for a mean vector under general conditions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1051-1062, November.
    3. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Mikhail Freer, 2019. "Revealed Preference Analysis of Expected Utility Maximization under Prize-Probability Trade-Offs," Working Papers ECARES 2019-27, ULB -- Universite Libre de Bruxelles.
    4. Mark M. Meerschaert & Hans-Peter Scheffler, 1999. "Sample Covariance Matrix for Random Vectors with Heavy Tails," Journal of Theoretical Probability, Springer, vol. 12(3), pages 821-838, July.
    5. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Mikhail Freer, 2018. "Equilibrium Play in First Price Auctions: Revealed Preference Analysis," Working Papers ECARES 2018-36, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Freer, Mikhail, 2022. "Revealed preference analysis of expected utility maximization under prize-probability trade-offs," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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