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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| Vydáno v: | Journal of the American Statistical Association Ročník 111; číslo 516; s. 1705 - 1714 |
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| Jazyk: | angličtina |
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Alexandria
Taylor & Francis
01.12.2016
Taylor & Francis Group,LLC Taylor & Francis Ltd |
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| ISSN: | 0162-1459, 1537-274X, 1537-274X |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Narisetty, Naveen N. Nair, Vijayan N. |
| Author_xml | – sequence: 1 givenname: Naveen N. surname: Narisetty fullname: Narisetty, Naveen N. email: naveennn@umich.edu organization: Department of Statistics, University of Michigan – sequence: 2 givenname: Vijayan N. surname: Nair fullname: Nair, Vijayan N. organization: Department of Statistics, University of Michigan |
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| SubjectTerms | Central regions Data Data depth equations Functional boxplots Outlier detection probability Property Regions Regression analysis Simultaneous inference Statistics Theory and Methods Usefulness |
| Title | Extremal Depth for Functional Data and Applications |
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