Another look at halfspace depth: flag halfspaces with applications

Dušan Pokorný, Petra Laketa and Stanislav Nagy

Journal of Nonparametric Statistics, 2024, vol. 36, issue 1, 165-181

Abstract: The halfspace depth is a well-studied tool of nonparametric statistics in multivariate spaces. We introduce a flag halfspace – an intermediary between a closed halfspace and its interior – and demonstrate that the halfspace depth can be equivalently formulated also in terms of flag halfspaces. Flag halfspaces allow us to derive theoretical results regarding the halfspace depth without the need to differentiate absolutely continuous measures from measures containing atoms, as was frequently done previously. Flag halfspaces are used to state results on the dimensionality of the halfspace median set for random samples. We prove that under mild conditions, the dimension of the sample halfspace median set of d-variate data cannot be d−1 and that for d = 2, the sample halfspace median set must be either a two-dimensional convex polygon or a data point.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2023.2236721 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:36:y:2024:i:1:p:165-181

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2023.2236721

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().