Asymptotics of generalized depth-based spread processes and applications

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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 languageEnglish (US)
Pages (from-to)363-380
Number of pages18
JournalJournal of Multivariate Analysis
Volume169
DOIs
StatePublished - Jan 1 2019

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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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