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On the Studentisation of Random Vectors

Author

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  • Vu, H. T. V.
  • Maller, R. A.
  • Klass, M. J.

Abstract

We give general matrix Studentisation results for random vectors converging in distribution to a spherically symmetric random vector, which have wide applicability to the asymptotic properties of estimators obtained from estimating equations, for example. Appropriate matrix "square roots," required for normalisation of the random vectors, are shown to be the Cholesky square root and the symmetric positive definite square root.

Suggested Citation

  • Vu, H. T. V. & Maller, R. A. & Klass, M. J., 1996. "On the Studentisation of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 142-155, April.
    • Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:142-155
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    Citations

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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. 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.
    3. Kesten, Harry & Maller, R. A., 1997. "Random Deletion Does Not Affect Asymptotic Normality or Quadratic Negligibility," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 136-179, October.
    4. H. Vu & R. Maller & X. Zhou, 1998. "Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 627-653, December.
    5. Csörgő, Miklós & Martsynyuk, Yuliya V., 2011. "Functional central limit theorems for self-normalized least squares processes in regression with possibly infinite variance data," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2925-2953.
    6. 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.
    7. Maller, Ross A. & Mason, David M., 2015. "Matrix normalized convergence of a Lévy process to normality at zero," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2353-2382.

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