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Sample Covariance Matrix for Random Vectors with Heavy Tails

Author

Listed:
  • Mark M. Meerschaert

    (University of Nevada)

  • Hans-Peter Scheffler

    (University of Dortmund)

Abstract

We compute the asymptotic distribution of the sample covariance matrix for independent and identically distributed random vectors with regularly varying tails. If the tails of the random vectors are sufficiently heavy so that the fourth moments do not exist, then the sample covariance matrix is asymptotically operator stable as a random element of the vector space of symmetric matrices.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021688101621
    DOI: 10.1023/A:1021688101621
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    References listed on IDEAS

    as
    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, S. J., 1994. "Asymptotics for Multivariate t-Statistic and Hotelling's T2-Statistic Under Infinite Second Moments via Bootstrapping," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 41-54, April.
    3. 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.
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