de Haan, L.; Resnick, Sidney I. Estimating the limit distribution of multivariate extremes. (English) Zbl 0777.62036 Commun. Stat., Stochastic Models 9, No. 2, 275-309 (1993). 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 \(\widehat\nu_ n\). Reviewer: W.Dziubdziela (Wrocław) Cited in 40 Documents MSC: 62G05 Nonparametric estimation 60G70 Extreme value theory; extremal stochastic processes 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics Keywords:consistency; domain of attraction; multivariate extreme value distribution; empirical measure; second order condition; asymptotic normality PDFBibTeX XMLCite \textit{L. de Haan} and \textit{S. I. Resnick}, Commun. Stat., Stochastic Models 9, No. 2, 275--309 (1993; Zbl 0777.62036) Full Text: DOI