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## Abstract:

We propose $L^p$ distance-based goodness-of-ﬁt (GOF) tests for uniform stochastic ordering with two continuous distributions $F$ and $G$, both of which are unknown. Our tests are motivated by the fact that when $F$ and $G$ are uniformly stochastically ordered, the ordinal dominance curve $R = FG−1$ is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable conﬁguration of $F$ and $G$ for $p \in [1, \infty]$. We use simulation to assess ﬁnite-sample performance and demonstrate that a modiﬁed, one-sample version of our procedure (e.g., with G known) is more powerful than the one-sample GOF test suggested by Arcones and Samaniego (2000, Annals of Statistics). We also discuss sample size determination. We illustrate our methods using data from a pharmacology study evaluating the eﬀects of administering caﬀeine to prematurely born infants.