Asymptotics of generalized depth-based spread processes and applications

Jin Wang

doi:10.1016/j.jmva.2018.09.012

Asymptotics of generalized depth-based spread processes and applications

Jin Wang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we study the asymptotic behavior of generalized depth-based spread processes, which include the scale curve of Liu et al. (1999) as a special case. Both uniform strong and weak convergences of the generalized depth-based spread processes are established. As applications, we obtain the asymptotic distributions of some nonparametric multivariate kurtosis measures. Applications to compare spread and kurtosis of two multivariate data sets, and to assess multivariate normality, are also discussed.

Original language	English (US)
Pages (from-to)	363-380
Number of pages	18
Journal	Journal of Multivariate Analysis
Volume	169
DOIs	https://doi.org/10.1016/j.jmva.2018.09.012
State	Published - Jan 2019

Keywords

Asymptotics
Depth function
Generalized spread process
Multivariate kurtosis
Multivariate normality
Nonparametric method
Scale curve

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2018.09.012

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keywords = "Asymptotics, Depth function, Generalized spread process, Multivariate kurtosis, Multivariate normality, Nonparametric method, Scale curve",

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AB - In this paper, we study the asymptotic behavior of generalized depth-based spread processes, which include the scale curve of Liu et al. (1999) as a special case. Both uniform strong and weak convergences of the generalized depth-based spread processes are established. As applications, we obtain the asymptotic distributions of some nonparametric multivariate kurtosis measures. Applications to compare spread and kurtosis of two multivariate data sets, and to assess multivariate normality, are also discussed.

KW - Asymptotics

KW - Depth function

KW - Generalized spread process

KW - Multivariate kurtosis

KW - Multivariate normality

KW - Nonparametric method

KW - Scale curve

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Asymptotics of generalized depth-based spread processes and applications

Abstract

Keywords

ASJC Scopus subject areas

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