Generalized Jackknife Semi-Parametric Estimators of the Tail Index

M. Ivette Gomes, M. Joao Martins and Manuela Neves

Abstract: In this paper we shall consider a natural Generalized Jackknife estimator of the index of regular variation $\gamma$ of a heavy right-tail $1-F(x)$, as $x\rightarrow+\infty $, associated to any adequate semi-parametric estimator of $\gamma$. Such an estimator is merely a linear combination of the original estimator at two different levels. We also study such a general linear combination asymptotically, and an illustration of how these results work in practice is provided.

Keywords: Statistical Theory of Extremes; Semi-parametric estimation; Jackknife methodology.

Classification (MSC2000): 62G05, 62G32, 62E20.; 62F40, 65C05.

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