Some intriguing properties of Tukey's half-space depth
By S. Dutta, A. Ghosh, Probal Chaudhuri. 2012
70 citations recorded by the source corpus.
For multivariate data, Tukey's half-space depth is one of the most popular depth functions available in the literature. It is conceptually simple and satisfies several desirable properties of depth functions. The Tukey median, the multivariate median associated with the half-space depth, is also a well-known measure of center for multivariate data with several interesting properties. In this article, we derive and investigate some interesting properties of half-space depth and its associated multivariate median. These properties, some of which are counterintuitive, have important statistical consequences in multivariate analysis. We also investigate a natural extension of Tukey's half-space depth and the related median for probability distributions on any Banach space (which may be finite- or infinite-dimensional) and prove some results that demonstrate anomalous behavior of half-space depth in infinite-dimensional spaces.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0f1f22773b5920b6d0b59abddc3113e6399a0e12
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In Statistics and Probability
- Anirvan Chakraborty
- Probal Chaudhuri
- Pavlo Mozharovskyi
- Karl Mosler
- Francesca Molinari
- Arie Beresteanu
- Anil Kumar Ghosh
Citations in the corpus
- Choosing Among Notions of Multivariate Depth Statistics (2020, background): “For example, the halfspace depth and the projection depth satisfy the projection property, as well as the zonoid depth and the Mahalanobis depth; see Dyckerhoff (2004). The projection property (22) allows to approximate a depth value from above by evaluating the univariate depth of projected data at”
- On data depth in infinite dimensional spaces (2014, background): “Recently, it has been shown in Dutta et al. (2011) that HD has degenerate behaviour when the probability distribution of X = (X1, X2, . . .) is such that X1, X2, . . . are independent random variables satisfying suitable moment conditions.”