论文标题
样品最大值的半参数概率分布估计器
A semiparametric probability distribution estimator of sample maximums
论文作者
论文摘要
已经研究了几种非参数推断的方法。这项研究调查了样品最大值的半参数概率分布估计。 Moriyama（2021）澄清说，随着尾巴的变化，对广义极值分布的参数拟合变得很大，这意味着收敛变得慢。 Moriyama（2021）提出了一个非参数分布估计器，而无需分布并获得渐近特性。事实证明，非参数估计器的灯塔数据效率超过了参数拟合估计器。此外，已经证明，在其他情况下，参数拟合估计器在数值上优于非参数。 在研究的激励下，我们构建了样品最大值的两种类型的半参数分布估计器。提出的分布估计量是通过混合Moriyama中提出的两个分布估计器（2021）来构建的。交叉验证方法和最大似然方法是作为估计最佳混合比的一种方式。仿真实验阐明了两种类型的半参数分布估计器的数值特性。
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.
