# Halfspace depth for general measures: the ray basis theorem and its consequences

```@article{Laketa2021HalfspaceDF,
title={Halfspace depth for general measures: the ray basis theorem and its consequences},
author={Petra Laketa and Stanislav Nagy},
journal={Statistical Papers},
year={2021}
}```
• Published 31 May 2021
• Mathematics
• Statistical Papers
The halfspace depth is a prominent tool of nonparametric multivariate analysis. The upper level sets of the depth, termed the trimmed regions of a measure, serve as a natural generalization of the quantiles and inter-quantile regions to higher-dimensional spaces. The smallest non-empty trimmed region, coined the halfspace median of a measure, generalizes the median. We focus on the (inverse) ray basis theorem for the halfspace depth, a crucial theoretical result that characterizes the halfspace…

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