Abstract #300488

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JSM 2002 Abstract #300488
Activity Number: 202
Type: Topic Contributed
Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics*
Abstract - #300488
Title: Volume Functionals and Skewness Measures in Nonparametric Multivariate Analysis
Author(s): Robert Serfling*+
Affiliation(s): University of Texas, Dallas
Address: , Richardson , Texas, 75083, USA
Keywords: Nonparametric Multivariate Analysis ; Skewness ; Dispersion ; Asymmetry
Abstract:

In terms of a given median-oriented quantile function, central regions of increasing probability generate a corresponding "volume functional," which characterizes in a certain way the spread of the underlying multivariate distribution. The various roles of this functional, and the asymptotic behavior of the sample volume functional, will be discussed. In particular, the volume functional supports formulation of a new nonparametric multivariate skewness functional which generalizes classical univariate skewness measures and yields corresponding new indices of asymmetry, weak and strong qualitative notions of skewness, and quantitative skewness measures in the multivariate context. Properties of all these entities will be discussed, along with the asymptotic behavior of empirical versions.

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