Geman-McClure中位数

Geman-McClure Medians

本文基于深度函数介绍了一类仿射等价的多元中位数.证明了所提的中位数的影响函数是有界的,且其渐近增加崩溃点能达到0.5.给出了Geman-McClure中位数的相合性和渐近正态性.模拟研究说明了所提中位数的有限样本表现,且能同时实现高的有效性和稳健性.最后,应用所提的方法分析了一个实际数据.

In this paper, we introduce a class of affine equivariant multivariate medians based on depth functions. We show that the influence function of the proposed medians is bounded, and the asymptotic addition breakdown point can achieve 0.5. Consistency and asymptotic normality of the Geman-McClure medians are established. Simulation studies are conducted to examine the performance of the proposed medians, and illustrate that the Geman-McClure medians can achieve high efficiency and robustness simultaneously. Finally, we apply the proposed methodology to analyze a real dataset.