NONPARAMETRIC GOODNESS-OF-FIT TESTS FOR UNIFORM STOCHASTIC ORDERING

• 成果类型: Article
• 署名作者: Tang, Chuan-Fa; Wang, Dewei; Tebbs, Joshua M.
• 署名单位: University of South Carolina System; University of South Carolina Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1535
• 发表日期: 2017
• 页码: 2565-2589
• 关键词: survival functions; likelihood; inference; curve; distributions; constraint

摘要

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 is an element of [1, infinity]. 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.