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Activity Number: 72 - Recent Advances in Nonparametric Statistical Methods II
Type: Contributed
Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #330426 Presentation
Title: Asymptotics of Generalized Depth-Based Scale Processes and Applications
Author(s): Jin Wang*
Companies: Northern Arizona University
Keywords: Asymptotics; Generalized scale process; Depth function; Multivariate kurtosis; Multivariate normality; Nonparametric method
Abstract:

To characterize the spread of a multivariate data set, Liu, Parelius and Singh (1999) introduced the depth-based scale curve but left its properties open. Here we study the asymptotic behavior of generalized depth-based scale processes, which include the scale curve of Liu, Parelius and Singh as a special case. The uniform strong and weak convergences of the generalized depth-based scale processes are established. As applications, we obtain asymptotic distributions of some nonparametric multivariate kurtosis measures. Applications to assess multivariate normality and compare two multivariate data sets with respect to kurtosis will also be discussed.


Authors who are presenting talks have a * after their name.

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