Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law
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.
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Volume (Year): 82 (2012)
Issue (Month): 12 ()
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References listed on IDEAS
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- 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.
- 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.
- 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.
- 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.
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