Multivariate Dispersion, Central Regions, and Depth: The Lift Zonoid Approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Lecture Notes in Statistics
165 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applications. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chapters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are collected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of multivariate analysis. Chapter 3 introduces a family of central regions, the zonoid trimmed regions, by which a distribution is characterized. Its sample version proves to be useful in describing data. Chapter 4 is devoted to a new notion of data depth, zonoid depth, which has applications in data analysis as well as in inference. In Chapter 5 nonparametric multivariate tests for location and scale are investigated; their test statistics are based on notions of data depth, including the zonoid depth. Chapter 6 introduces the depth of a hyperplane and tests which are built on it. Chapter 7 is about volume statistics, the volume of the lift zonoid and the volumes of zonoid trimmed regions; they serve as multivariate measures of dispersion and dependency. Chapter 8 treats the lift zonoid order, which is a stochastic order to compare distributions for their dispersion, and also indices and related orderings |
| Beschreibung: | 1 Online-Ressource (X, 291p) |
| ISBN: | 9781461300458 9780387954127 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4613-0045-8 |
Internformat
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| 245 | 1 | 0 | |a Multivariate Dispersion, Central Regions, and Depth |b The Lift Zonoid Approach |c by Karl Mosler |
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| 490 | 1 | |a Lecture Notes in Statistics |v 165 |x 0930-0325 | |
| 500 | |a This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applications. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chapters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are collected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of multivariate analysis. Chapter 3 introduces a family of central regions, the zonoid trimmed regions, by which a distribution is characterized. Its sample version proves to be useful in describing data. Chapter 4 is devoted to a new notion of data depth, zonoid depth, which has applications in data analysis as well as in inference. In Chapter 5 nonparametric multivariate tests for location and scale are investigated; their test statistics are based on notions of data depth, including the zonoid depth. Chapter 6 introduces the depth of a hyperplane and tests which are built on it. Chapter 7 is about volume statistics, the volume of the lift zonoid and the volumes of zonoid trimmed regions; they serve as multivariate measures of dispersion and dependency. Chapter 8 treats the lift zonoid order, which is a stochastic order to compare distributions for their dispersion, and also indices and related orderings | ||
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Datensatz im Suchindex
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| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-1-4613-0045-8 |
| format | Electronic eBook |
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| isbn | 9781461300458 9780387954127 |
| issn | 0930-0325 |
| language | English |
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| spelling | Mosler, Karl Verfasser aut Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach by Karl Mosler New York, NY Springer New York 2002 1 Online-Ressource (X, 291p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 165 0930-0325 This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applications. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chapters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are collected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of multivariate analysis. Chapter 3 introduces a family of central regions, the zonoid trimmed regions, by which a distribution is characterized. Its sample version proves to be useful in describing data. Chapter 4 is devoted to a new notion of data depth, zonoid depth, which has applications in data analysis as well as in inference. In Chapter 5 nonparametric multivariate tests for location and scale are investigated; their test statistics are based on notions of data depth, including the zonoid depth. Chapter 6 introduces the depth of a hyperplane and tests which are built on it. Chapter 7 is about volume statistics, the volume of the lift zonoid and the volumes of zonoid trimmed regions; they serve as multivariate measures of dispersion and dependency. Chapter 8 treats the lift zonoid order, which is a stochastic order to compare distributions for their dispersion, and also indices and related orderings Statistics Mathematical statistics Economics / Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Statistical Theory and Methods Statistik Wirtschaft Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Wahrscheinlichkeitsmaß (DE-588)4137556-7 s 1\p DE-604 Lecture Notes in Statistics 165 (DE-604)BV036592911 165 https://doi.org/10.1007/978-1-4613-0045-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mosler, Karl Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach Lecture Notes in Statistics Statistics Mathematical statistics Economics / Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Statistical Theory and Methods Statistik Wirtschaft Multivariate Analyse (DE-588)4040708-1 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4137556-7 |
| title | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach |
| title_auth | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach |
| title_exact_search | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach |
| title_full | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach by Karl Mosler |
| title_fullStr | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach by Karl Mosler |
| title_full_unstemmed | Multivariate Dispersion, Central Regions, and Depth The Lift Zonoid Approach by Karl Mosler |
| title_short | Multivariate Dispersion, Central Regions, and Depth |
| title_sort | multivariate dispersion central regions and depth the lift zonoid approach |
| title_sub | The Lift Zonoid Approach |
| topic | Statistics Mathematical statistics Economics / Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Statistical Theory and Methods Statistik Wirtschaft Multivariate Analyse (DE-588)4040708-1 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| topic_facet | Statistics Mathematical statistics Economics / Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Statistical Theory and Methods Statistik Wirtschaft Multivariate Analyse Wahrscheinlichkeitsmaß |
| url | https://doi.org/10.1007/978-1-4613-0045-8 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT moslerkarl multivariatedispersioncentralregionsanddepththeliftzonoidapproach |