Title: An optimal transportation approach for assessing almost stochastic order,
Abstract: When stochastic dominance $F\leq_{st}G$ 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, $\mathcal W_2$, to stochastic
order of these trimmed versions. Our characterization for that distance
naturally leads to consider a $\mathcal W_2$-based index of disagreement with
stochastic order, $\varepsilon_{\mathcal W_2}(F,G)$. We provide asymptotic
results allowing to test $H_0: \varepsilon_{\mathcal W_2}(F,G)\geq
\varepsilon_0$ vs $H_a: \varepsilon_{\mathcal W_2}(F,G)<\varepsilon_0$, 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.