A Topologically Valid Definition of Depth for Functional Data
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Alicia Nieto-Reyes [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Statistical science - Hayward, Calif. : Inst., 1986, 31(2016), 1, Seite 61-79 |
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| Übergeordnetes Werk: |
volume:31 ; year:2016 ; number:1 ; pages:61-79 |
| Links: |
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| DOI / URN: |
10.1214/15-STS532 |
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| 520 | |a The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. | ||
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| 650 | 4 | |a Topological manifolds | |
| 650 | 4 | |a Data analysis | |
| 650 | 4 | |a Statistical methods | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a multivariate statistics | |
| 650 | 4 | |a Functional data | |
| 650 | 4 | |a robustness | |
| 650 | 4 | |a partial observability | |
| 650 | 4 | |a statistical depth | |
| 700 | 0 | |a Heather Battey |4 oth | |
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10.1214/15-STS532 doi PQ20160430 (DE-627)OLC1974043320 (DE-599)GBVOLC1974043320 (PRQ)p1449-99e1b450f59f8d2fc1cf8f414532424bc9bee076c7878ba4b35212f53e4a548a0 (KEY)0151760020160000031000100061topologicallyvaliddefinitionofdepthforfunctionalda DE-627 ger DE-627 rakwb eng 510 DNB 31.73 bkl Alicia Nieto-Reyes verfasserin aut A Topologically Valid Definition of Depth for Functional Data 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics Topological manifolds Data analysis Statistical methods Multivariate analysis multivariate statistics Functional data robustness partial observability statistical depth Heather Battey oth Enthalten in Statistical science Hayward, Calif. : Inst., 1986 31(2016), 1, Seite 61-79 (DE-627)129199435 (DE-600)54152-7 (DE-576)014457032 0883-4237 nnns volume:31 year:2016 number:1 pages:61-79 http://dx.doi.org/10.1214/15-STS532 Volltext http://search.proquest.com/docview/1771234411 http://projecteuclid.org/euclid.ss/1455115914 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_31 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_2061 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4700 31.73 AVZ AR 31 2016 1 61-79 |
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10.1214/15-STS532 doi PQ20160430 (DE-627)OLC1974043320 (DE-599)GBVOLC1974043320 (PRQ)p1449-99e1b450f59f8d2fc1cf8f414532424bc9bee076c7878ba4b35212f53e4a548a0 (KEY)0151760020160000031000100061topologicallyvaliddefinitionofdepthforfunctionalda DE-627 ger DE-627 rakwb eng 510 DNB 31.73 bkl Alicia Nieto-Reyes verfasserin aut A Topologically Valid Definition of Depth for Functional Data 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics Topological manifolds Data analysis Statistical methods Multivariate analysis multivariate statistics Functional data robustness partial observability statistical depth Heather Battey oth Enthalten in Statistical science Hayward, Calif. : Inst., 1986 31(2016), 1, Seite 61-79 (DE-627)129199435 (DE-600)54152-7 (DE-576)014457032 0883-4237 nnns volume:31 year:2016 number:1 pages:61-79 http://dx.doi.org/10.1214/15-STS532 Volltext http://search.proquest.com/docview/1771234411 http://projecteuclid.org/euclid.ss/1455115914 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_31 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_2061 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4700 31.73 AVZ AR 31 2016 1 61-79 |
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10.1214/15-STS532 doi PQ20160430 (DE-627)OLC1974043320 (DE-599)GBVOLC1974043320 (PRQ)p1449-99e1b450f59f8d2fc1cf8f414532424bc9bee076c7878ba4b35212f53e4a548a0 (KEY)0151760020160000031000100061topologicallyvaliddefinitionofdepthforfunctionalda DE-627 ger DE-627 rakwb eng 510 DNB 31.73 bkl Alicia Nieto-Reyes verfasserin aut A Topologically Valid Definition of Depth for Functional Data 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics Topological manifolds Data analysis Statistical methods Multivariate analysis multivariate statistics Functional data robustness partial observability statistical depth Heather Battey oth Enthalten in Statistical science Hayward, Calif. : Inst., 1986 31(2016), 1, Seite 61-79 (DE-627)129199435 (DE-600)54152-7 (DE-576)014457032 0883-4237 nnns volume:31 year:2016 number:1 pages:61-79 http://dx.doi.org/10.1214/15-STS532 Volltext http://search.proquest.com/docview/1771234411 http://projecteuclid.org/euclid.ss/1455115914 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_31 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_2061 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4700 31.73 AVZ AR 31 2016 1 61-79 |
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10.1214/15-STS532 doi PQ20160430 (DE-627)OLC1974043320 (DE-599)GBVOLC1974043320 (PRQ)p1449-99e1b450f59f8d2fc1cf8f414532424bc9bee076c7878ba4b35212f53e4a548a0 (KEY)0151760020160000031000100061topologicallyvaliddefinitionofdepthforfunctionalda DE-627 ger DE-627 rakwb eng 510 DNB 31.73 bkl Alicia Nieto-Reyes verfasserin aut A Topologically Valid Definition of Depth for Functional Data 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics Topological manifolds Data analysis Statistical methods Multivariate analysis multivariate statistics Functional data robustness partial observability statistical depth Heather Battey oth Enthalten in Statistical science Hayward, Calif. : Inst., 1986 31(2016), 1, Seite 61-79 (DE-627)129199435 (DE-600)54152-7 (DE-576)014457032 0883-4237 nnns volume:31 year:2016 number:1 pages:61-79 http://dx.doi.org/10.1214/15-STS532 Volltext http://search.proquest.com/docview/1771234411 http://projecteuclid.org/euclid.ss/1455115914 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_31 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_2061 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4700 31.73 AVZ AR 31 2016 1 61-79 |
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10.1214/15-STS532 doi PQ20160430 (DE-627)OLC1974043320 (DE-599)GBVOLC1974043320 (PRQ)p1449-99e1b450f59f8d2fc1cf8f414532424bc9bee076c7878ba4b35212f53e4a548a0 (KEY)0151760020160000031000100061topologicallyvaliddefinitionofdepthforfunctionalda DE-627 ger DE-627 rakwb eng 510 DNB 31.73 bkl Alicia Nieto-Reyes verfasserin aut A Topologically Valid Definition of Depth for Functional Data 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. Nutzungsrecht: © Copyright 2016 Institute of Mathematical Statistics Topological manifolds Data analysis Statistical methods Multivariate analysis multivariate statistics Functional data robustness partial observability statistical depth Heather Battey oth Enthalten in Statistical science Hayward, Calif. : Inst., 1986 31(2016), 1, Seite 61-79 (DE-627)129199435 (DE-600)54152-7 (DE-576)014457032 0883-4237 nnns volume:31 year:2016 number:1 pages:61-79 http://dx.doi.org/10.1214/15-STS532 Volltext http://search.proquest.com/docview/1771234411 http://projecteuclid.org/euclid.ss/1455115914 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_31 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_2061 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4266 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4700 31.73 AVZ AR 31 2016 1 61-79 |
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The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. |
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The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. |
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The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function. |
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