标题： 空间符号协方差算子：渐近结果和应用 显示英文标题

标题： The spatial sign covariance operator: Asymptotic results and applications

摘要： 由于记录能力的不断提高，功能数据分析已成为一个重要研究课题。 对于功能数据，关于异常值检测和/或稳健统计过程的发展最近才开始。 样本协方差算子的一个稳健替代方法是样本空间符号协方差算子。 在本文中，我们研究当位置未知时样本空间符号协方差算子的渐近行为。 在获得结果的其他可能应用中，我们推导了从样本空间符号协方差算子得到的主要方向的渐近分布，并开发了检测两个总体散射算子之间差异的检验。 特别是，通过一个小样本尺寸的蒙特卡罗研究说明了检验性能。 显示英文摘要

摘要： Due to the increasing 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 has started recently. One robust alternative to the sample covariance operator is the sample spatial sign covariance operator. In this paper, we study the asymptotic behaviour of the sample spatial sign covariance operator when location is unknown. Among other possible applications of the obtained results, we derive the asymptotic distribution of the principal directions obtained from the sample spatial sign covariance operator and we develop test to detect differences between the scatter operators of two populations. In particular, the test performance is illustrated through a Monte Carlo study for small sample sizes.