报告题目：Maximum likelihood estimation in transformed linear regression with non-normal error

报 告 人：北京师范大学 童行伟 教授

报告时间：2019年3月7日（周四）上午10:00-12:00

报告地点：数学与统计学院310会议室

    摘要：This paper discusses the transformed linear regression with nonnormal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution, respectively. Despite the popularity and generality of linear transformation models, however, there is no general theory on the maximum likelihood estimation of the regression parameter and the transformation function. One main difficulty for this is that the transformation function near the tails diverges to infinity and can be quite unstable. It affects the accuracy of the estimation of the transformation function and regression parameters. In this paper, we develop the maximum likelihood estimation approach and provide the near optimal conditions on the error distribution under which the consistency and asymptotic normality of the resulting estimators can be established. Extensive numerical studies suggest that the methodology works well, and an application to the data on typhoon forecast is provided.

    报告人简介：童行伟，北京师范大学统计学院数理统计系主任、教授、博士生导师。2003年毕业于北京大学概率统计系获统计学博士学位。2003-至今，在北京师范大学工作。2005-2006年在美国密苏里大学Columbia分校从事博士后研究。现为中国现场统计研究会高维数据统计分会秘书长、北京师范大学彩票研究中心研究员。主要从事生物统计、金融统计、稳健统计等领域的教学和研究工作，在Biometrika、Biometrics、Statistica Sinica等国内外知名期刊发表学术论文60余篇，其中SCI论文40余篇，出版教材《高等统计学》1部，译著两部。主持研究国家自然科学基金面上项目、国家自然科学基金重点项目子课题以及教育部科学技术研究重大项目等10余项。