Robust Estimation through Schoenberg transformations

TL;DR

This paper introduces a robust location estimation method based on Schoenberg transformations, which leverage Euclidean distances to produce flexible, stable estimates applicable to various data dimensions.

Contribution

It presents a novel robust estimation approach using Schoenberg transformations, generalizing M-estimators with theoretical guarantees and practical illustrations.

Findings

The method depends solely on Euclidean distances.

Two solution regimes are identified and analyzed.

The approach is demonstrated on real data sets.

Abstract

Schoenberg transformations, mapping Euclidean configurations into Euclidean configurations, define in turn a transformed inertia, whose minimization produces robust location estimates. The procedure only depends upon Euclidean distances between observations, and applies equivalently to univariate and multivariate data. The choice of the family of transformations and their parameters defines a flexible location strategy, generalizing M-estimators. Two regimes of solutions are identified. Theoretical results on their existence and stability are provided, and illustrated on two data sets.