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Publication
Peaks over random threshold methodology for tail index and high quantile estimation
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Advisor(s)
Abstract(s)
In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity
of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class
of estimators is based on the sample of excesses over a random threshold, originating
what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study.
Description
Keywords
Heavy tails High quantiles Semi-parametric estimation Linear property Sample of excesses
Citation
SANTOS, Paulo Araújo ; ALVES, M. Isabel Fraga ; GOMES, M. Ivette - Peaks over random threshold methodology for tail index and high quantile estimation. Revstat. ISSN 1645-6726. Vol. 4, no. 3 (Nov. 2006), p. 227-247
Publisher
Instituto Nacional de Estatística