报告简介  Abstract

This paper discusses the transformed linear regression with non-normal 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 a typhoon forecast is provided.

嘉宾简介  About the Speaker

童行伟，北京师范大学统计学院教授，博士生导师。主要从事生物统计，金融统计等方向的研究。中国现场统计研究会常务理事，概率统计学会常务理事；主持一项科技部重点研发计划子课题，主持国家自然基金面上项目3项，教育部重大科研项目1项，目前发表近50篇SCI论文。

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