主 题：Density Estimation in the Two-sample Problem with Likelihood Ratio Ordering
主讲人：Tao Yu 博士
主持人：林华珍教授
时 间：2015年5月18日（星期一）下午3:30-4:30
地 点：通博楼B座212学术会议室
主办单位：统计研究中心 统计学院 科研处
主讲人简介：
Tao Yu is Assistant Professor, Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546. Pengfei Li is Associate Professor, Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo, ON, Canada, N2L 3G1(Email: pengfei.li@uwaterloo.ca). Jing Qin is Mathematical Statistician, National Institute of Allergy and Infectious Diseases, National Institutes of Health, 6700B Rockledge Drive MSC 7609, Bethesda, MD 20892 (Email: jingqin@niaid.nih.gov).
内容提要：
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 monotonic. Such a problem is well motivated from medical data and has been widely identiffed in the literature.However, effective methods for solving this problem are not yet available in the community. Clearly, an effectively method should at least satisfy (1) the resulting estimates are probability densities; (2) the corresponding density ratio inherits the monotonic property, otherwise it is diffcult to explain the analysis results. In this paper, we propose estimates for these densities whose ratio inherits the monotonic property, and explore their theoretical properties. One interesting application of our density estimates is that the corresponding receiver operating characteristic (ROC) curve estimate is concave.Through numerical studies, we observe that both the density estimates and the ROC curve estimate from our method outperform their competitors, particularly when the sample size is relatively small.
