Moment Estimator for Random Vectors with Heavy Tails

If a set of independent, identically distributed random vectors has heavy tails, so that the covariance matrix does not exist, there is no reason to expect that the sample covariance matrix conveys useful information. On the contrary, this paper shows that the eigenvalues and eigenvectors of the sam...

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Bibliographic Details
Published in:Journal of multivariate analysis 1999, Vol.71 (1), p.145-159
Main Authors: Meerschaert, Mark M., Scheffler, Hans-Peter
Format: Article
Language:English
Subjects:
60E07
62F12
62H11
90A09
Applications
Exact sciences and technology
generalized domains of attraction
heavy tails
Insurance, economics, finance
Mathematics
operator stable laws
operator stable laws generalized domains of attraction regular variation heavy tails
Probability and statistics
regular variation
Sciences and techniques of general use
Statistics
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Description
Summary:If a set of independent, identically distributed random vectors has heavy tails, so that the covariance matrix does not exist, there is no reason to expect that the sample covariance matrix conveys useful information. On the contrary, this paper shows that the eigenvalues and eigenvectors of the sample covariance matrix contain detailed information about the probability tails of the data. The eigenvectors indicate a set of marginals which completely determine the moment behavior of the data, and the eigenvalues can be used to estimate the tail thickness of each marginal. The paper includes an example application to a data set from finance.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1999.1835