Extremal Depth for Functional Data and Applications

We propose a new notion called "extremal depth" (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme "outlyingness." ED has several desirable properties that are not shared by ot...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2016-12, Vol.111 (516), p.1705-1714
Main Authors: Narisetty, Naveen N., Nair, Vijayan N.
Format: Article
Language:English
Subjects:
Central regions
Data depth
Functional boxplots
Outlier detection
Regression analysis
Simultaneous inference
Statistics
Theory and Methods
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Summary:We propose a new notion called "extremal depth" (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme "outlyingness." ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous coverage probability; (b) there is a correspondence between ED-based (simultaneous) central regions and appropriate pointwise central regions; and (c) the method is resistant to certain classes of functional outliers. The article examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. Supplementary materials for this article are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2015.1110033