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Asymptotics of generalized depth-based spread processes and applications

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  • Wang, Jin

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.

Suggested Citation

  • Wang, Jin, 2019. "Asymptotics of generalized depth-based spread processes and applications," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 363-380.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:363-380
    DOI: 10.1016/j.jmva.2018.09.012
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    References listed on IDEAS

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    11. Wang, Jin & Serfling, Robert, 2006. "Influence functions for a general class of depth-based generalized quantile functions," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 810-826, April.
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    Cited by:

    1. Petra Laketa & Stanislav Nagy, 2022. "Halfspace depth for general measures: the ray basis theorem and its consequences," Statistical Papers, Springer, vol. 63(3), pages 849-883, June.
    2. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.

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