TY - JOUR
AU - El Methni, Jonathan
AU - Girard, Stéphane
PY - 2024/01/19
Y2 - 2024/09/07
TI - A Refined Extreme Quantile Estimator for Weibull Tail-distributions: Accepted - January 2024
JF - REVSTAT-Statistical Journal
JA - REVSTAT
VL -
IS -
SE - Forthcoming Paper
DO -
UR - https://revstat.ine.pt/index.php/REVSTAT/article/view/668
SP -
AB - <p><span dir="ltr" role="presentation">We address the estimation of extreme quantiles of Weibull tail-distributions.</span> <span dir="ltr" role="presentation">Since such </span><span dir="ltr" role="presentation">quantiles are asymptotically larger than the sample maximum, their estimation requires extrap</span><span dir="ltr" role="presentation">olation methods.</span> <span dir="ltr" role="presentation">In the case of Weibull tail-distributions, classical extreme-value estimators </span><span dir="ltr" role="presentation">are numerically outperformed by estimators dedicated to this set of light-tailed distributions. </span><span dir="ltr" role="presentation">The latter estimators of extreme quantiles are based on two key quantities: an order statistic </span><span dir="ltr" role="presentation">to estimate an intermediate quantile and an estimator of the Weibull tail-coefficient used to </span><span dir="ltr" role="presentation">extrapolate.</span> <span dir="ltr" role="presentation">The common practice is to select the same intermediate sequence for both esti</span><span dir="ltr" role="presentation">mators.</span> <span dir="ltr" role="presentation">We show how an adapted choice of two different intermediate sequences leads to a r</span><span dir="ltr" role="presentation">eduction of the asymptotic bias associated with the resulting refined estimator. This analy</span><span dir="ltr" role="presentation">sis is supported by an asymptotic normality result associated with the refined estimator.</span> <span dir="ltr" role="presentation">A </span><span dir="ltr" role="presentation">data-driven method is introduced for the practical selection of the intermediate sequences and </span><span dir="ltr" role="presentation">our approach is compared to three estimators of extreme quantiles dedicated to Weibull tail-</span><span dir="ltr" role="presentation">distributions on simulated data.</span> <span dir="ltr" role="presentation">An illustration on a real data set of daily wind measures is </span><span dir="ltr" role="presentation">also provided.</span></p>
ER -