Empirical Likelihood based Confidence Regions for first order parameters of a heavy tailed distribution - Mathematics > Statistics Theory

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Abstract: Let $X 1, \ldots, X n$ be some i.i.d. observations from a heavy taileddistribution $F$, i.e. such that the common distribution of the excesses over ahigh threshold $u n$ can be approximated by a Generalized Pareto Distribution$G {\gamma,\sigma n}$ with $\gamma >0$. This work is devoted to the problem offinding confidence regions for the couple $\gamma,\sigma n$ : combining theempirical likelihood methodology with estimation equations close but notidentical to the likelihood equations introduced by J. Zhang Australian andNew Zealand J. Stat n.491, 2007, asymptotically valid confidence regions for$\gamma,\sigma n$ are obtained and proved to perform better than Wald-typeconfidence regions especially those derived from the asymptotic normality ofthe maximum likelihood estimators. By profiling out the scale parameter,confidence intervals for the tail index are also derived.

Autor: Julien Worms LMV, Rym Worms LAMA

Fuente: https://arxiv.org/