Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation
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,...
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Published in | Revstat Vol. 4; no. 3 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Instituto Nacional de Estatística | Statistics Portugal
01.11.2006
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1645-6726 2183-0371 |
DOI: | 10.57805/revstat.v4i3.37 |