Depth-Based Recognition of Shape Outlying Functions. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Nagy, Stanislav; Gijbels, Irène; Hlubinka, Daniel
• Is Part Of: Journal of computational and graphical statistics. Volume 26:Issue 4(2017)
• Page Start: 883
• Page End: 893
• Publication Date: 2017-10-02
• Subjects: Data depth -- Functional data -- Infimal depth -- Integrated depth -- Outlying functions -- Shape outliers; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1336445
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: 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.