Estimation of the tail exponent of multivariate regular variation
It is well known that the extreme behavior of multivariate observations can be characterized by a spectral measure and a tail exponent. The estimation of this latter quantity is considered here, which is grounded on the fact that every convex combination of a random vector having a multivariate regularly varying tail also has a univariate regularly varying tail with the same exponent (under certain conditions). Specifically, the proposed estimator of the tail exponent is obtained from a weighted average of Hill's estimators obtained for all convex combinations of the given random vector. The asymptotic properties of this estimator together with its finite sample performance are considered. An illustration with financial data concludes the manuscript.
scientific article; zbMATH DE number 6807778
scientific article