Tail index estimation in models of generalized order statistics. (English) Zbl 1073.62047
Summary: This article is concerned with generalized order statistics based on a distribution function \(F\) which belongs to the domain of attraction of the Fréchet distribution \(G_{\alpha}\), \(\alpha >0\). We consider the B. M. Hill [Ann. 3, 1163–1174 (1975; Zbl 0323.62033)] estimator of \(\alpha\) which is based on extreme and intermediate generalized order statistics. Under suitable conditions its consistency and asymptotic normality are shown.
MSC:
| 62G32 | Statistics of extreme values; tail inference |
| 62G30 | Order statistics; empirical distribution functions |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
asymptotic normality; domain of attraction; generalized order statistics; Hill estimator; tail indexCitations:
Zbl 0323.62033References:
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