A topologically valid construction of depth for functional data
针对函数型数据深度构造中缺乏合理对称性概念的问题，提出了拓扑有效的对称性定义及相应的深度概念，并证明其满足已有公理体系。
Numerous problems remain in the construction of statistical depth for functional data. Issues stem largely from the absence of a well-conceived notion of symmetry. The present paper proposes a topologically valid notion of symmetry for distributions on functional metric spaces and a corresponding notion of depth. The latter is shown to satisfy the axiomatic definition of functional depth introduced by Nieto-Reyes and Battey (2016).