Year: 2025
Type: article
Abstract: We compute the robustness of Fermat–Weber points with respect to any finite gauge. We show a breakdown point of $$1/(1+\sigma )$$ 1 / ( 1 + σ ) where $$\sigma $$ σ is the asymmetry measure of the gauge. We obtain quantitative results indicating how far a corrupted Fermat–Weber point can lie from the true value in terms of the original sample and the size of the corrupted part. If the distance from the true value depends only on the original sample, then we call the gauge ‘uniformly robust.’ We show that polyhedral gauges are uniformly robust, but locally strictly convex norms are not, while in dimension 2 any uniform robust gauge is polyhedral.
Source: Mathematical Programming
Authors: Andrei Comăneci, Frank Plastria
Institutions: Technische Universität Berlin, Vrije Universiteit Brussel
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4416566651