Open Access
December 2017 Nonparametric goodness-of-fit tests for uniform stochastic ordering
Chuan-Fa Tang, Dewei Wang, Joshua M. Tebbs
Ann. Statist. 45(6): 2565-2589 (December 2017). DOI: 10.1214/16-AOS1535


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 [Ann. Statist. 28 (2000) 116–150]. 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.


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Chuan-Fa Tang. Dewei Wang. Joshua M. Tebbs. "Nonparametric goodness-of-fit tests for uniform stochastic ordering." Ann. Statist. 45 (6) 2565 - 2589, December 2017.


Received: 1 May 2016; Revised: 1 September 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838143
MathSciNet: MR3737902
Digital Object Identifier: 10.1214/16-AOS1535

Primary: 62G10
Secondary: 62F30

Keywords: Brownian bridge , hazard rate ordering , least favorable distribution , order-restricted inference , ordinal dominance curve , star-shaped ordering

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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