A Multivariate Hill Estimator
نویسندگان
چکیده
We propose a simple and semi-parametric estimator for the tail index of a regular varying elliptical random vector. Since, for univariate random variables, our estimator boils down to the Hill estimator and it inherits the simplicity and asymptotic properties, we name it after Bruce M. Hill. The estimator is based on the distance between an elliptical probability contour and the outer – or exceedance– observations. The Minimum Covariance Determinant method, which is suitable for large dimensions, provides the probability ellipsoid. A Monte Carlo study and an empirical illustration to 21 world-wide financial market indexes show that the multivariate Hill estimator works well in practice.
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