Density estimation in the two-sample problem with likelihood ratio ordering

• 成果类型: Article
• 署名作者: Yu, Tao; Li, Pengfei; Qin, Jing
• 署名单位: National University of Singapore; University of Waterloo; National Institutes of Health (NIH) - USA; NIH National Institute of Allergy & Infectious Diseases (NIAID)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw069
• 发表日期: 2017
• 页码: 141152
• 关键词: operating characteristic curves; malaria attributable fractions; tests; MODEL

摘要

In this paper, we propose a method for estimating the probability density functions in a two-sample problem where the ratio of the densities is monotone. This problem has been widely identified in the literature, but effective solution methods, in which the estimates should be probability densities and the corresponding density ratio should inherit monotonicity, are unavailable. If these conditions are not satisfied, the applications of the resultant density estimates might be limited. We propose estimates for which the ratio inherits the monotonicity property, and we explore their theoretical properties. One implication is that the corresponding receiver operating characteristic curve estimate is concave. Through numerical studies, we observe that both the density estimates and the receiver operating characteristic curve estimate from our method outperform those resulting directly from kernel density estimates, particularly when the sample size is relatively small.