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Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law

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  • Martsynyuk, Yuliya V.

Abstract

Assuming that the sample correlation matrix of vector X converges to a positive definite nonstochastic matrix, we establish a uniform Euclidean norm approximation in probability and a functional CLT for a multivariate Student process, based on independent copies of X. These results obtain if and only if X is in the generalized domain of attraction of the multivariate normal law.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2270-2277
    DOI: 10.1016/j.spl.2012.08.008
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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. 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.
    3. 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.
    4. 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.
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