Multivariate Dispersion, Central Regions, and Depth

The Lift Zonoid Approach

Karl Mosler - Collection Lecture Notes in Statistics

306 pages, parution le 05/09/2002

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Résumé

The lift zonoid approach is based on a new representation of probability measures: a d-variate probability measure is represented by a convex set, its lift zonoid. First, lift zonoids are useful in data analysis to describe an empirical distribution by central (so- called trimmed) regions. They give rise to a concept of data depth related to the mean which is also useful in nonparametric tests for location and scale. Second, for comparing random vectors, the set inclusion of lift zonoids defines a stochastic order that reflects the dispersion of random vectors. This has many applications to stochastic comparison problems in economics and other fields.

This monograph ves the first account in book form of the theory of lift zonoids and demonstrates its usefulness in multivariate analysis. Chapter 1 offers the reader an informal introduction to basic ideas, Chapter 2 presents a comprehensive investigation into the theory. The remaining seven chapters treat 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.

L'auteur - Karl Mosler

Mosler, K., Universität zu Köln, Germany
Karl Mosler is Professor of Statistics and Econometrics at the University of Cologne. He is Editor of the Allgemeines Statistisches Archive, Journal of the German Statistical Society, and has authored numerous research articles and four books (all with Springer-Verlag) in statistics and operations research.

Sommaire

Introduction
Zonoids and lift zonoids
Central regions
Data depth
Inference based on data depth
Depth of hyperplanes
Volume statistics
Orderings and indices of dispersion
Measuring economic disparity and concentration.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Karl Mosler
Collection	Lecture Notes in Statistics
Parution	05/09/2002
Nb. de pages	306
Format	15,5 x 23,5
Couverture	Broché
Poids	458g
Intérieur	Noir et Blanc
EAN13	9780387954127
ISBN13	978-0-387-95412-7