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.
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Meerschaert, M.M., Scheffler, HP. Sample Covariance Matrix for Random Vectors with Heavy Tails. Journal of Theoretical Probability 12, 821–838 (1999). https://doi.org/10.1023/A:1021688101621
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DOI: https://doi.org/10.1023/A:1021688101621