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Asymptotics of generalized depth-based spread processes and applications. (English) Zbl 1409.62107

Summary: In this paper, we study the asymptotic behavior of generalized depth-based spread processes, which include the scale curve of R. Y. Liu et al. [Ann. Stat. 27, No. 3, 783–858 (1999; Zbl 0984.62037)] 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0984.62037

Software:

DepthProc
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Full Text: DOI

References:

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