Estimating the limit distribution of multivariate extremes

Laurens de Haan · Sidney I. Resnick

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Probability and Risk Models Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

Consider a random sample from a multivariate distribution F(x) which is in the domain of attraction of a multivariate extreme value distribution G(x). Based on we construct an empirical measure which is a consistent estimator for — log G. In an appendix, we explore a second order strengthening of the standard multivariate domain of attraction condition and under this second order condition, we prove our estimator is asymptotically normal in a suitably strong sense

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References

1987Extreme Values, Regular Variation and Point Processes 1989A Moment Estimator for the Index of an Extreme-Value Distribution 1988Bivariate Extreme Value Theory: Models and Estimation 1977Limit theory for multivariate sample extremes 1977Max-infinite divisibility

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