Lecture on“Density estimation in the two-sample problem with likelihood ratio ordering”
Speaker: Li peng fei
Date：December 30, 2016
Time: 3:00 pm-4:00 pm
Location: The conference room on the second floor
Sponsor: School Of Statistici QFNU
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).