B0914
Title: Heavy-tailed extremile regression in risky seismic areas
Authors: Thibault Laurent - Universite Toulouse 1 Capitole (France) [presenting]
Abdelaati Daouia - Toulouse School of Economics (France)
Gilles Stupfler - ENSAI and CREST (France)
Abstract: Extremile regression defines a least-squares analogue of quantile regression as is the case in the duality between the conditional mean and the conditional median. The use of extremiles appears naturally in risk handling where they enjoy various intuitive meanings in terms of weighted moments rather than tail probabilities. They account for the magnitude of infrequent observations and not only for their relative frequency. They belong to both classes of concave distortion risk measures and coherent spectral risk measures of law--invariant type. We study the implications of extremile regression for estimating tail risk, focusing on heavy-tailed seismic distributions in risky areas. Based on a localized and averaged Hill estimator of the underlying conditional tail index, we present extrapolated estimators for high conditional extremiles and derive their asymptotic normality under mild conditions. In a simulation study, we examine their performance on finite samples in comparison with a method based on a kernel smoothing estimator of the conditional tail index. On an earthquake dataset in Indonesia and its surroundings in the Indian Ocean, these estimators guarantee a more reasonable and prudent differentiation of the severity of massive earthquakes geographically compared to the traditional Value at Risk and Tail Conditional Mean.
