B0782
Title: Bias- and variance-corrected asymptotic Gaussian inference about extreme expectiles
Authors: Antoine Usseglio-Carleve - Avignon Université (France) [presenting]
Gilles Stupfler - University of Angers (France)
Abdelaati Daouia - Toulouse School of Economics (France)
Abstract: The expectile 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 behavior of extreme values as well as its excellent axiomatic properties. A series of recent papers have focused on expectile estimation at extreme levels, with a view to gathering essential information about low-probability, high-impact events that are of most interest to risk managers. Actual inference about extreme executives 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. The focus is on asymptotic Gaussian inference about tail expectiles in the challenging context of heavy-tailed observations. We use an in-depth analysis of the proofs of asymptotic normality results for two classes of extreme expectile estimators to derive bias- and variance-corrected Gaussian confidence intervals. These, unlike previous attempts in the literature, are well-rooted in statistical theory and can accommodate underlying distributions that display a wide range of tail behaviors. A large-scale simulation study and real data analyses confirm the versatility of the proposed technique.
