β-Skeleton depth functions and medians

Mengta Yang and Reza Modarres

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 20, 5127-5143

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1386320

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