Tests for stochastic ordering under biased sampling. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Chang, Hsin-wen; El Barmi, Hammou; McKeague, Ian W.
• Is Part Of: Journal of nonparametric statistics. Volume 28:Issue 4(2016)
• Page Start: 659
• Page End: 682
• Publication Date: 2016-10-01
• Subjects: Empirical likelihood -- length bias -- order-restricted inference -- size bias -- weighted distributions; 62G10 -- 62G20 -- 62G30; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2016.1225048
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: In two-sample comparison problems it is often of interest to examine whether one distribution function majorises the other, that is, for the presence of stochastic ordering. This paper develops a nonparametric test for stochastic ordering from size-biased data, allowing the pattern of the size bias to differ between the two samples. The test is formulated in terms of a maximally selected local empirical likelihood statistic. A Gaussian multiplier bootstrap is devised to calibrate the test. Simulation results show that the proposed test outperforms an analogous Wald-type test, and that it provides substantially greater power over ignoring the size bias. The approach is illustrated using data on blood alcohol concentration of drivers involved in car accidents, where the size bias is due to drunker drivers being more likely to be involved in accidents. Further, younger drivers tend to be more affected by alcohol, so in making comparisons with older drivers the analysis is adjusted for differences in the patterns of size bias.