Karl Mosler

Multivariate Dispersion, Central Regions, and Depth (eBook, PDF)

The Lift Zonoid Approach

• Format: PDF

Produktbeschreibung

This book has many applications to stochastic comparison problems in economics and other fields. It covers theory of lift zonoids and demonstrates its usefulness in multivariate analysis, an informal introduction to basic ideas, and a comprehensive investigation into the theory, as well as various applications of the lift zonoid approach and may be separately studied.

Readers are assumed to have a firm grounding in probability at the graduate level.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 292
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461300458
• Artikelnr.: 43992079

Autorenporträt

Karl Mosler, Universität zu Köln, Germany

Inhaltsangabe

Preface.- 1 Introduction.- 1.4 Examples of lift zonoids.- 1.5 Representing distributions by convex compacts.- 1.6 Ordering distributions.- 1.7 Central regions and data depth.- 1.8 Statistical inference.- 2 Zonoids and lift zonoids.- 2.1 Zonotopes and zonoids.- 2.2 Lift zonoid of a measure.- 2.3 Embedding into convex compacts.- 2.4 Continuity and approximation.- 2.5 Limit theorems.- 2.6 Representation of measures by a functional.- 2.7 Notes.- 3 Central regions.- 3.1 Zonoid trimmed regions.- 3.2 Properties.- 3.3 Univariate central regions.- 3.4 Examples of zonoid trimmed regions.- 3.5 Notions of central regions.- 3.6 Continuity and law of large numbers.- 3.7 Further properties.- 3.8 Trimming of empirical measures.- 3.9 Computation of zonoid trimmed regions.- 3.10 Notes.- 4 Data depth.- 4.1 Zonoid depth.- 4.2 Properties of the zonoid depth.- 4.3 Different notions of data depth.- 4.4 Combination invariance.- 4.5 Computation of the zonoid depth.- 4.6 Notes.- 5 Inference based on data depth (by Rainer Dyckerhoff).- 5.1 General notion of data depth.- 5.2 Two-sample depth test for scale.- 5.3 Two-sample rank test for location and scale.- 5.4 Classical two-sample tests.- 5.5 A new Wilcoxon distance test.- 5.6 Power comparison.- 5.7 Notes.- 6 Depth of hyperlanes.- 6.1 Depth of a hyperlane and MHD of a sample.- 6.2 Properties of MHD and majority depth.- 6.3 Combinatorial invariance.- 6.4 measuring combinatorial dispersion.- 6.5 MHD statistics.- 6.6 Significance tests and their power.- 6.7 Notes.- 7 Depth of hyperlanes.- 6.1 Depth of a hyperplane and MHD of a sample.- 6.2 Properties of MHD and majority depth.- 6.3 Combinatorial invariance.- 6.4 Measuring combinatorial dispersion.- 6.5 MHD statistics.- 6.6 Significance tests and their power.- 6.7 Notes.- 8 Orderings and indices of dispersion.- 8.1 Lift zonoid order.- 8.2 order of marginals and independence.- 8.3 Order of convolutions.- 8.4 Lift zonoid order vs. convex order.- 8.5 Volume inequalities and random determinants.- 8.6 Increasing, scaled, and centered orders.- 8.7 Properties of dispersion orders.- 8.8 Multivariate indices of dispersion.- 8.9 Notes.- 9 Economic disparity and concentration.- 9.1 Measuring economic inequality.- 9.2 Inverse Lorenz function (ILF).- 9.3 Price Lorenz order.- 9.4 Majorizations of absolute endowments.- 9.5 Other inequality orderings.- 9.6 Measuring industrial concentration.- 9.7 Multivariate concentration function.- 9.8 Multivariate concentration indices.- 9.9 Notes.- Appendix A: Basic notions.- Appendix B: Lift zonoids of bivariate normals.