Β-Skeleton depth functions and medians. Issue 20 (18th October 2018) - Yang, Mengta; Modarres, Reza
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.