2017-03-03

Dewei Wang, PhD, Department of Statistics, University of South Carolina

"Nonparametric goodness-of-fit tests for uniform stochastic ordering"

Motivated by a recent study of caffeine treatment on premature infants, we propose Lp 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 inspired 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,∞]. 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). We illustrate our methods using data from a pharmacology study evaluating the effects of administering caffeine to prematurely born infants.

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