报 告 人：王汉生 教授  

报告题目：Mixture Conditional Regression with Ultrahigh Dimensional Text Data for Estimating Extralegal Factor Effects

报告时间：2024年3月14日（周四） 上午10:00

报告地点：静远楼1506学术报告厅

主办单位：数学与统计学院、数学研究院、科学技术研究院

报告人简介： 

       王汉生，1998年北京大学数学学院概率统计系本科毕业，2001年美国威斯康星大学麦迪逊分校统计系博士毕业。2003年加入光华至今，历任副系主任（2007—2013），系主任（2013—2021）。国内外各种专业杂志上发表文章100+篇，并合著有英文专著共1本，（合）著中文教材3本。国家杰出青年基金获得者，全国工业统计学教学研究会青年统计学家协会创始会长，美国数理统计协会（IMS）Fellow，美国统计学会（ASA）Fellow，国际统计协会（ISI）Elected Member。先后历任9个国际学术期刊副主编（Associate Editor / Editor）。国内外各种专业杂志上发表文章100+篇，并合著有英文专著共1本，（合）著中文教材4本。

报告摘要: 

       Testing judicial impartiality is a problem of fundamental importance in empirical legal studies, for which standard regression methods have been popularly used to estimate the extralegal factor effects. However, those methods cannot handle control variables with ultrahigh dimensionality, such as those found in judgment documents recorded in text format. To solve this problem, we develop a novel mixture conditional regression (MCR) approach, assuming that the whole sample can be classified into a number of latent classes. Within each latent class, a standard linear regression model can be used to model the relationship between the response and a key feature vector, which is assumed to be of a fixed dimension. Meanwhile, ultrahigh dimensional control variables are then used to determine the latent class membership, where a na\ive Bayes type model is used to describe the relationship. Hence, the dimension of control variables is allowed to be arbitrarily high. A novel expectation-maximization algorithm is developed for model estimation. Therefore, we are able to estimate the key parameters of interest as efficiently as if the true class membership were known in advance. Simulation studies are presented to demonstrate the proposed MCR method. A real dataset of Chinese burglary offenses is analyzed for illustration purposes.