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：由于极值指数(EVI)控制着分布函数的尾部行为,对 EVI 的估计是极端值理论中一个非常重要的专题。最近对 EVI 的估计以及同系物的估计发展是在非参数回归的背景下发生的。然而,对于大范围的共变,完全非参数估计者面临着维度的诅咒问题。为了避免这种情况,我们在Pareto 类型尾部分布下对 EVI 的回归应用单一指数模型。我们研究了单一指数模型的受罚最大可能性估计。还开发了估计者的无症状特性。提出了数字研究,以显示拟议模型的效率。