Luca Trapin (Università di Bologna)

Tail index regression forest

Abstract. Regression analysis of the tail index has received increasing attention over the last few years. The availability of large and complex datasets has stimulated the development of tail index regression techniques that can capture complex relationships between a large number of predictors and a dependent variable of interest. However, available methods are either flexible and asymptotically justified but do not scale well with the dimension of the predictor space, or well-suited in high-dimension but lack asymptotic results. This paper presents a novel random forest approach that fills this gap. We establish the asymptotic normality of our tail index regression forest estimator under mild assumptions on the tail behavior of the dependent variable. An extensive simulation study and an application to the conditional distribution of ROE for a large cross-section of U.S. companies confirm that our approach outperforms existing parametric and non-parametric tail index regression methods.