Moment estimator for random vectors with heavy tails

@article{Meerschaert1999MomentEF,
  title={Moment estimator for random vectors with heavy tails},
  author={Mark M. Meerschaert and Hans-Peter Scheffler},
  journal={Journal of Multivariate Analysis},
  year={1999},
  volume={71},
  pages={145-159}
}
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 eigen- vectors indicate a set of marginals which completely determine the moment behavior of the data… 
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References

SHOWING 1-10 OF 33 REFERENCES
Sample Covariance Matrix for Random Vectors with Heavy Tails
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
Moving Averages of Random Vectors with Regularly Varying Tails
Regular variation is an analytic condition on the tails of a probability distribution which is necessary for an extended central limit theorem to hold, when the tails are too heavy to allow
Consistency of Hill's Estimator for Dependent Data
Consider a sequence of possibly dependent random variables having the same marginal distribution F, whose tail 1−F is regularly varying at infinity with an unknown index − α < 0 which is to be
Parameter and quantile estimation for the generalized pareto distribution
The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including
13 Financial applications of stable distributions
Measuring Tail Thickness to Estimate the Stable Index α: A Critique
A generalized Pareto or simple Pareto tail-index estimate above 2 has frequently been cited as evidence against infinite-variance stable distributions. It is demonstrated that this inference is
Linear Statistical Inference and its Applications.
Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation.
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable
...
...