Semiparametric Tail Index Regression

Abstract–Understanding why extreme events occur is often of major scientific interest in many fields. The occurrence of these events naturally depends on explanatory variables, but there is a severe lack of flexible models with asymptotic theory for understanding this dependence, especially when variables can affect the outcome nonlinearly. This article proposes a novel semiparametric tail index regression model to fill the gap for this purpose. We construct consistent estimators for both parametric and nonparametric components of the model, establish the corresponding asymptotic normality properties for these components that can be applied for further inference, and illustrate the usefulness of the model via extensive Monte Carlo simulation and the analysis of return on equity data and Alps meteorology data.