# Partial reconstruction of measures from halfspace depth

@inproceedings{Laketa2022PartialRO, title={Partial reconstruction of measures from halfspace depth}, author={Petra Laketa and Stanislav Nagy}, year={2022} }

. The halfspace depth of a d -dimensional point x with respect to a ﬁnite (or probability) Borel measure µ in 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 ∈ 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 R d . In this paper we show that…

## One Citation

### Another look at halfspace depth: Flag halfspaces with applications

- Mathematics
- 2022

. The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of a point with…

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