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A0636
Title: Heavy-tailed extremile regression in risky seismic areas Authors:  Abdelaati Daouia - Fondation Jean-Jacques Laffont (France) [presenting]
Thibault Laurent - Toulouse School of Economics (France)
Gilles Stupfler - University of Angers (France)
Abstract: Extremile regression defines a least-squares analog of quantile regression as is the case in the duality between the conditional mean and median. The use of extremiles appears naturally in risk mitigation where they enjoy various intuitive meanings in terms of weighted moments rather than tail probabilities. They account for the magnitude of infrequent events 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 their implications for estimating and inferring tail risk, focusing on heavy-tailed seismic distributions in risky areas. Based on a localized Hill estimator of the conditional tail index, we present an extrapolated estimator for high conditional extremiles and derive its asymptotic normality under mild conditions. This extremile estimator shows an excellent performance in simulations compared with the existing competitors. On an earthquake dataset, it suggests a more reasonable and prudent differentiation of the severity of massive earthquakes geographically compared to the traditional Value at Risk and Tail Conditional Mean.