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On the Studentisation of Random Vectors

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 57 (1996)
    Issue (Month): 1 (April)
    Pages: 142-155

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    Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:142-155

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    Related research

    Keywords: Studentisation random vectors spherically symmetric random vectors norming matrices stochastic matrices non-stochastic matrices positive definite matrices Cholesky square root symmetric square root (null);

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    Cited by:
    1. 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.
    2. 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.
    3. 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, vol. 50(4), pages 627-653, December.
    4. 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.

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