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.

翻译：极端值指数（EVI）控制着分布函数的尾部行为，因此EVI的估计是极值理论中非常重要的课题。近年来，伴随着协变量的EVI估计研究主要集中于非参数回归领域。然而，当协变量维度较高时，完全非参数估计方法会面临维数灾难问题。为规避这一困难，本文在帕累托型尾部分布假设下，将单指标模型应用于EVI回归。我们研究了单指标模型的惩罚最大似然估计方法，并推导了该估计量的渐近性质。数值研究展示了所提出模型的有效性。