A0834
Title: Bias- and variance-corrected asymptotic Gaussian inference about extreme expectiles
Authors: Abdelaati Daouia - Toulouse School of Economics (France)
Gilles Stupfler - University of Angers (France)
Antoine Usseglio-Carleve - Avignon Université (France) [presenting]
Abstract: The executile is a prime candidate for being a standard risk measure in actuarial and financial contexts for its ability to recover information about probabilities and typical behaviour of extreme values as well as its excellent axiomatic properties. A series of recent papers have focused on executile estimation at extreme levels, with a view to gathering essential information about low-probability. These high-impact events are of most interest to risk managers. Actual inference about extreme executiles is a difficult question, however, due to their least squares formulation making them very sensitive to tail heaviness, even though the obtention of accurate confidence intervals is paramount if the expectile risk measure is to be used in practical applications. This article focuses on asymptotic Gaussian inference about tail expectiles in the challenging context of heavy-tailed observations. An in-depth analysis of the proofs of asymptotic normality results is used for two classes of extreme expectile estimators to derive bias- and variance-corrected Gaussian confidence intervals. Unlike previous attempts in the literature, these are well-rooted in statistical theory and can accommodate underlying distributions that display a wide range of tail behaviours. A large-scale simulation study and real data analyses confirm the versatility of the proposed technique.
