Depth-Based Recognition of Shape Outlying Functions
针对现有深度函数难以识别形状异常函数的问题，提出一种简单修改方法，无需数据可微性假设，保留原深度的一致性等优良性质，并在多个示例中验证其有效性。
A major drawback of many established depth functionals is their ineffectiveness in identifying functions outlying merely in shape. Herein, a simple modification of functional depth is proposed to provide a remedy for this difficulty. The modification is versatile, widely applicable, and introduced without imposing any assumptions on the data, such as differentiability. It is shown that many favorable attributes of the original depths for functions, including consistency properties, remain preserved for the modified depths. The powerfulness of the new approach is demonstrated on a number of examples for which the known depths fail to identify the outlying functions. Supplementary material for this article is available online.