An Optimal Transportation Approach for Assessing Almost Stochastic Order

By Eustasio del Barrio, Juan Antonio Cuesta-Albertos, Carlos Matrán. 2017

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When stochastic dominance does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the \(L_2\)–Wasserstein distance, \(\mathscr {W}_2\), to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a \(\mathscr {W}_2\)-based index of disagreement with stochastic order, \(\varepsilon _{\mathscr {W}_2}(F,G)\). We provide asymptotic results allowing to test \(H_0: \varepsilon _{\mathscr {W}_2}(F,G)\ge \varepsilon _0\) versus \(H_a: \varepsilon _{\mathscr {W}_2}(F,G)<\varepsilon _0\), that, under rejection, would give statistical guarantee of almost stochastic dominance. We include a simulation study showing a good performance of the index under the normal model.

Subfields: Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e5dd4fd0918cf941f16ce96ed6b4c2272c6843cb