Partial reconstruction of measures from halfspace depth
Petra Laketa; Stanislav Nagy · 2022 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
The study found no significant effect — useful as a negative control or null benchmark for your own design.
Abstract (excerpt)
The halfspace depth of a $d$-dimensional point $x$ with respect to a finite (or probability) Borel measure $μ$ in $\mathbb{R}^d$ is defined as the infimum of the $μ$-masses of all closed halfspaces containing $x$. A natural question is whether the halfspace depth, as a function of $x \in \mathbb{R}^d$, determines the measure $μ$ completely. In general, it turns out that this is not the case, and it is possible for two different measures to have the same halfspace depth function everywhere in $\mathbb{R}^d$. In this paper we show that despite this negative result, one can still obtain a substan
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Metadata source: arXiv