B1163
Title: Inference for extremal regression with dependent heavy-tailed data
Authors: Gilles Stupfler - University of Angers (France) [presenting]
Antoine Usseglio-Carleve - Avignon Université (France)
Abdelaati Daouia - Toulouse School of Economics (France)
Abstract: Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. A fully operational inferential theory is developed for extreme conditional quantiles and expectiles in the challenging framework of strong mixing, conditional heavy-tailed data whose tail index may vary with covariate values. It requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling difficulties inherent to mixing, smoothing, and sparsity associated with covariate localization. The pointwise asymptotic normality of the estimators is proven, and optimal rates of convergence reminiscent of those found in the i.i.d. regression setting are obtained but have not been established in the conditional extreme value literature. The assumptions hold in a wide range of models. Full bias and variance reduction procedures are proposed, and simple but effective data-based rules for selecting tuning hyperparameters are used. The inference strategy is shown to perform well in finite samples and is showcased in applications to stock returns and tornado loss data.
