Statistical Depth Function Random Variables for Univariate Distributions and induced Divergences

Rui Ding

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arXiv · 2304.13091

Statistical Depth Function Random Variables for Univariate Distributions and induced Divergences

Rui Ding

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Abstract

In this paper, we show that the halfspace depth random variable for samples from a univariate distribution with a notion of center is distributed as a uniform distribution on the interval [0,1/2]. The simplicial depth random variable has a distribution that first-order stochastic dominates that of the halfspace depth random variable and relates to a Beta distribution. Depth-induced divergences between two univariate distributions can be defined using divergences on the distributions for the statistical depth random variables in-between these two distributions. We discuss the properties of such induced divergences, particularly the depth-induced TVD distance based on halfspace or simplicial depth functions, and how empirical two-sample estimators benefit from such transformations.

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BibTeX RIS

Rui Ding. 2023-04-25. Statistical Depth Function Random Variables for Univariate Distributions and induced Divergences. https://arxiv.org/abs/2304.13091

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