Several approaches of nonparametric inference for extreme values have been studied. This study surveys the semiparametric probability distribution estimation of sample maximums. Moriyama (2021) clarified that the parametric fitting to the generalized extreme value distribution becomes large as the tail becomes light, which means the convergence becomes slow. Moriyama (2021) proposed a nonparametric distribution estimator without the fitting of the distribution and obtained asymptotic properties. The nonparametric estimator was proved to outperform the parametrically fitting estimator for light-tailed data. Moreover, it was demonstrated that the parametric fitting estimator numerically outperformed the nonparametric one in other cases. Motivated by the study, we construct two types of semiparametric distribution estimators of sample maximums. The proposed distribution estimators are constructed by mixing the two distribution estimators presented in Moriyama (2021). The cross-validation method and the maximum-likelihood method are presented as a way of estimating the optimal mixing ratio. Simulation experiments clarify the numerical properties of the two types of semiparametric distribution estimators.
翻译:研究了若干极端值的非对称推算方法,这项研究调查了抽样最大值的半对称概率分布估计。Moriyama (2021年)澄清说,随着尾巴变轻,与普遍极端值分布相匹配的参数就会大,这意味着趋同速度会缓慢。Moriyama (2021年)提议了一个非对称分布估计仪,而没有对分布进行适当调整并获得无症状特性。非对称估测仪被证明优于光尾数数据的对准估计仪。此外,还表明,在其他情况下,与普遍极端值分布相匹配的参数在数字上优于非对称的参数。在研究的推动下,我们建造了两种类型的样本最大半对称分布估计仪。拟议的分布估计仪是混合在Moriyama(2021年)中提出的两个分布估计仪的。交叉校准方法和最大类似方法被证明为估计最佳混合比率的一种方法。模拟实验澄清了两种半对称分布估计器的两种类型的半对称分布估计器的数字属性。