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β-Skeleton depth functions and medians

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  • Mengta Yang
  • Reza Modarres

Abstract

We define the β-skeleton depth based on the probability that a point is contained within the β-skeleton influence region of two i.i.d. random vectors. The proposed family of depth functions satisfies the four desirable properties of statistical depth function. We also define and examine the sample β-skeleton depth functions and show that they share well-behaved asymptotic properties, including uniform consistency and asymptotic normality. Finally, we explore the β-skeleton multidimensional medians as location estimators of the center of multivariate distributions, discuss its asymptotic properties, and study its breakdown point. A Monte Carlo study compares the β-skeleton medians with the random Tukey median and the sample mean.

Suggested Citation

  • Mengta Yang & Reza Modarres, 2018. "β-Skeleton depth functions and medians," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(20), pages 5127-5143, October.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:20:p:5127-5143
    DOI: 10.1080/03610926.2017.1386320
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