Single-index models for extreme value index regression

Abstract: Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have been in the context of nonparametric regression. However, for the large dimension of covariates, the fully nonparametric estimator faces the problem of the curse of dimensionality. To avoid this, we apply the single index model to EVI regression under Pareto-type tailed distribution. We study the penalized maximum likelihood estimation of the single index model. The asymptotic properties of the estimator are also developed. Numerical studies are presented to show the efficiency of the proposed model.