Sample Covariance Matrix for Random Vectors with Heavy Tails

Mark M. Meerschaert () and Hans-Peter Scheffler ()
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Mark M. Meerschaert: University of Nevada
Hans-Peter Scheffler: University of Dortmund

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 821-838

Abstract: 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.

Keywords: Operator stable; generalized domains of attraction; regular variation; sample covariance matrix; heavy tails (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021688101621

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