Abstract

In this article, we propose the median-of-means type nonparametric estimator for S-Gini index by using the idea of grouping under the massive data framework, which has been widely used in economics, finance, and insurance. Under certain condition on the growing rate of the number of subgroups, the consistency and asymptotic normality of proposed estimator are investigated. Furthermore, we construct a new method to test S-Gini index based on the empirical likelihood method for median. Our method avoids any prior estimate of variance structure of proposed estimator, which is difficult to estimate and often causes much inaccuracy. Numerical simulations and a real data analysis are designed to show the performance of our estimator. It is shown that the new proposed estimator is quite robust with respect to outliers.

摘要

本文利用海量数据框架下的分组思想，提出了S-基尼指数的中位数型非参数估计量，该估计量已广泛应用于经济、金融、保险等领域。在子群数量增长率一定的条件下，研究了所提出的估计量的一致性和渐近正态性。此外，我们基于中位数的经验似然法构建了一种新的S-基尼指数检验方法。我们的方法避免了对所提出的估计器的方差结构的任何先前估计，这很难估计并且通常会导致很大的不准确性。数值模拟和真实数据分析旨在显示我们的估计器的性能。结果表明，新提出的估计量对于异常值非常稳健。