Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied and with much experimental success, little theoretical progress has been made in analysing functional depths. This article highlights how the common $h$-depth and related statistical depths for functional data can be viewed as a kernel mean embedding, a technique used widely in statistical machine learning. This connection facilitates answers to open questions regarding statistical properties of functional depths, as well as it provides a link between the depth and empirical characteristic function based procedures for functional data.

翻译：统计深度是衡量一个点的代表性与参考概率度的比较。深度允许对多变量或功能空间中的数据进行排序和排序。虽然应用广泛,实验性也非常成功,但在分析功能深度方面没有取得多少理论进展。本条着重说明了如何将功能数据的共同的美元深度和相关统计深度视为内核中嵌,这是统计机学习中广泛使用的一种技术。这种连接有助于回答关于功能深度统计特性的公开问题,并提供了功能数据深度和经验特征功能程序之间的联系。