报告题目：Density estimation in the two-sample problem with likelihood ratio ordering

报告人：李鹏飞

主办单位：统计学院

时间：12月30日下午15:00-16:00

地点：科技楼二楼北会议室

Abstract：In this talk, we discuss the 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 monotonic property, and we explore their theoretical properties. One application 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. This talk is based on the joint paper, Yu, Li, and Qin (2016, Biometrika, in press).

李鹏飞教授简介：加拿大滑铁卢大学统计与精算系教授，研究兴趣广泛，研究领域包括混合模型、渐进理论、经验似然、大脑影像数据分析、平滑技术、带约束的统计推断等，近几年在统计学领域的专业期刊发表论文30余篇，其中包括在统计学四大顶级期刊 The Annals of Statistics, Journal of the Royal Statistical Society: Series B, Journal of the American Statistical Association, Biometrika上发表论文10余篇。