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Estimating the limit distribution of multivariate extremes. (English) Zbl 0777.62036

Let \(\{\underline{X}_ n=(X_{n1},\dots,X_{nd})\), \(n\geq 1\}\) be i.i.d. random vectors with \(d\)-dimensional distribution function \(F(\underline{x})\) which is in the domain of attraction of a multivariate extreme value distribution \(G(\underline{x})\). The authors propose an estimator \(\widehat \nu_ n\) for \(-\log G\) which is an empirical measure constructed by \(\underline{X}_ 1,\dots,\underline{X}_ n\). They show that the estimator \(\widehat\nu_ n\) is weakly and strongly consistent and, under some second order condition on \(F\), discuss asymptotic normality of \(\widehat\nu_ n\).

MSC:

62G05 Nonparametric estimation
60G70 Extreme value theory; extremal stochastic processes
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
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