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Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

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  • Steven J. Sepanski

    (Saginaw Valley State University)

Abstract

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.

Suggested Citation

  • Steven J. Sepanski, 1997. "Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law," Journal of Theoretical Probability, Springer, vol. 10(4), pages 1053-1063, October.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:4:d:10.1023_a:1022622902495
    DOI: 10.1023/A:1022622902495
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    References listed on IDEAS

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    1. Meerschaert, Mark M., 1993. "Regular variation and generalized domains of attraction in k," Statistics & Probability Letters, Elsevier, vol. 18(3), pages 233-239, October.
    2. 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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