Efficiency and breakdown point of the symmetrized-cost barycenter

Determine the efficiency curve and breakdown point of the barycenter obtained by minimizing the symmetrized Pal–Wong transport cost over the probability simplex.

Background

The paper introduces the symmetrized Pal–Wong transport cost as a smooth, symmetric approximation to the Hilbert projective metric. Its loss has a quadratic behavior near the diagonal and linear tails, yielding a Huber-type robust barycenter with bounded gross-error sensitivity. The paper establishes existence and uniqueness for interior observations and analyzes influence behavior, but does not characterize the estimator’s efficiency as a function of the underlying distribution or determine its finite-sample or asymptotic breakdown point.