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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 853-880

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\centerline{\large\bf ESTIMATING THE EXTREME VALUE INDEX AND HIGH}
\vspace{2pt}
\centerline{\large\bf QUANTILES WITH EXPONENTIAL REGRESSION}
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\centerline{\large\bf MODELS}
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\author{G. Matthys and J. Beirlant}
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\centerline{\it Katholieke Universiteit Leuven}
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\begin{quotation}
\noindent {\it Abstract:}
In this paper we present exponential regression models for spacings, or ordered
excesses over a given threshold, and for log-ratios of such spacings under
maximum domain of attraction conditions. From these we derive estimators for
the extreme value index (EVI) and for high quantiles, which share many
attractive properties of the maximum likelihood estimators from the
\hbox{peaks-over-thresholds} method, but offer the extra advantage of being
generally applicable without restriction on the value of the EVI. Further, the
exponential regression models can be refined with parameters of second order
regular variation, which reduces the bias of the resulting estimators. The
refined models also give rise to insightful and practical techniques to select
the threshold in the estimation of the EVI and of high quantiles.
We demonstrate asymptotic normality of the newly proposed estimators and
compare their small sample behaviour to some classical methods in a simulation
study.\par
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\noindent {\it Key words and phrases:}
Bias correction, peaks-over-thresholds method, second order regular variation,
threshold selection.
\end{quotation}
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