  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.
