论文标题
极值索引回归的单索引模型
Single-index models for extreme value index regression
论文作者
论文摘要
由于极值指数（EVI）控制了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主题。估计EVI以及协变量的最新发展是在非参数回归的背景下。但是，对于协变量的较大维度，完全非参数估计器面临着维度诅咒的问题。为了避免这种情况，我们将单个索引模型应用于帕累托型尾部分布下的EVI回归。我们研究了单个指数模型的惩罚最大似然估计。还开发了估计量的渐近特性。提出了数值研究以显示所提出模型的效率。
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.
