|
Activity Number:
|
103
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Monday, August 4, 2008 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
Section on Nonparametric Statistics
|
| Abstract - #300971 |
|
Title:
|
A Nonparametric Kurtosis Ordering for Multivariate Distributions
|
|
Author(s):
|
Jin Wang*+ and Weihua Zhou
|
|
Companies:
|
Northern Arizona University and The University of North Carolina, Charlotte
|
|
Address:
|
Department of Mathematics and Statistics, Flagstaff, AZ, 86011-5717,
|
|
Keywords:
|
Nonparametric method ; Volume functional ; Kurtosis ; Ordering ; Elliptically symmetric distributions ; Multivariate normality
|
|
Abstract:
|
Extending the Balanda and MacGillivray (1990) kurtosis ordering for univariate distributions, we define and study a nonparametric kurtosis ordering for multivariate distributions. This ordering is preserved by the nonparametric multivariate kurtosis functional of Wang and Serfling (2005) and it is inversely preserved by the "fan plot" of Liu, Parelius and Singh (1999). For elliptically symmetric distributions, the ordering determines the distribution up to affine equivalence. This is applied to design a new graphical method to assess multivariate normality. Ordering results are established for three important families of elliptically symmetric distributions: Kotz-type distributions, Pearson Type VII distributions, and Pearson Type II distributions.
|
