The spatial sign covariance operator: Asymptotic results and applications
The spatial sign covariance operator: Asymptotic results and applications
复制标题
空间符号协方差算子：渐近结果和应用
DOI：
10.1016/j.jmva.2018.10.002
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
M. Sued
中科院分区：
文献类型：
--
作者：
G. Boente;Daniela Rodriguez;M. Sued
由于记录能力的增加，功能数据分析已成为一个重要的研究课题。对于功能数据，异常值检测的研究和/或稳健统计程序的开发最近才开始。样本协方差算子的一种稳健替代方法是样本空间符号协方差算子。在本文中，我们研究以估计位置为中心的样本空间符号协方差算子的渐近行为。在我们的结果的可能应用中，我们推导了从样本空间符号协方差算子获得的主方向的渐近分布，并开发了一个测试程序来检测两个总体的散布算子之间的差异。测试性能通过小样本量的蒙特卡罗研究来说明。
Due to increased recording capability, functional data analysis has become an important research topic. For functional data, the study of outlier detection and/or the development of robust statistical procedures started only recently. One robust alternative to the sample covariance operator is the sample spatial sign covariance operator. In this paper, we study the asymptotic behavior of the sample spatial sign covariance operator centered at an estimated location. Among possible applications of our results, we derive the asymptotic distribution of the principal directions obtained from the sample spatial sign covariance operator and we develop a testing procedure to detect differences between the scatter operators of two populations. The test performance is illustrated through a Monte Carlo study for small sample sizes.