**统计与管理学院2017年学术报告第73期****【主 题】****Semiparametric inferences for dominance index under density ratio model****【报告人】**Chen Jiahua 教授University of British Columbia

**【时 间】**2017年12月16日（星期六）10:00-11:00**【地 点】**上海财经大学统计与管理学院大楼1208会议室【

**摘 要**】One important and often discussed research problem in statistics is how to compare several populations; examples arise in medical science, engineering, finance and more. Often population means or medians are compared. However, one population may have a larger mean not because of a widely spread wealthy but a small number of super-rich individuals. The mean income therefore may not reflect wealth of the general population.Instead, an index on the degree of stochastic dominance of one population over another better reflects the relative wealthy. Currently, there is no generic estimator of this index with known asymptotic distribution but one obtained under restrictive conditions.We suggest linking the populations via a density ratio model. Under this model,we develop an empirical likelihood estimator and establish its asymptotically normality.In addition, the estimation efficiency is enhanced by exploring the similarities between the populations. Furthermore, we provide a valid bootstrap approach for hypothesis testing and the construction of confidence intervals. Simulation experiments show that the proposed estimator substantially improves the estimation efficiency and the power of the test, and it leads to confidence intervals with satisfactorily precise coverage probabilities.Two examples are included to demonstrate the usefulness of both the method and the concept.Joint work with Weiwei ZhuangUniversity of Science and Technology of China, Hefei, Anhui, China 230026 and Boyi Hu University of British Columbia