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Descriptive measures of multivariate scatter and linear dependence

✍ Scribed by Daniel Peña; Julio Rodrı́guez

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
248 KB
Volume
85
Category
Article
ISSN
0047-259X

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✦ Synopsis

In this paper we propose two new descriptive measures for multivariate data: the effective variance and the effective dependence. These measures have a direct geometric and statistical interpretation and can be used to compare groups with different number of variables. The contribution of these measures to understanding multivariate data is illustrated by several examples.

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Nonparametric notions of multivariate ``scatter measure'' and ``more scattered,'' based on statistical depth functions, are investigated. In particular, notions of ``more scattered'' based on the ``halfspace'' depth function are shown to generalize versions introduced by P. J. Bickel and E. L. Lehma