Multivariate Dispersion, Central Regions, and Depth
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Multivariate Dispersion, Central Regions, and Depth

Multivariate Dispersion, Central Regions, and Depth


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About the Book

This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applica- tions. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chap- ters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are col- lected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of multivariate analysis. Chap- ter 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 in- vestigated; 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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Product Details
  • ISBN-13: 9780387954127
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Depth: 19
  • Height: 234 mm
  • No of Pages: 292
  • Series Title: Lecture Notes in Statistics
  • Sub Title: The Lift Zonoid Approach
  • Width: 156 mm
  • ISBN-10: 0387954120
  • Publisher Date: 10 Jul 2002
  • Binding: Paperback
  • Edition: Softcover reprint of the original 1st ed. 2002
  • Language: English
  • Returnable: N
  • Spine Width: 17 mm
  • Weight: 494 gr


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