报告摘要：

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the EM estimation of the regression and change point parameters. The existence of the random change point is detected by the supremum (SUP) test of score statistics. Theoretically, we establish the convergency and asymptotic distribution of the estimation, and show that the EM estimates converge in distribution to normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance.

报告人简介：

童行伟，北京师范大学教授，博士生导师，目前担任北京师范大学数理统计系系主任、教育心理与数据科学技术与应用广东省普通高校重点实验室主任。博士毕业于北京大学数学科学学院，美国University of Missouri, Columbia 博士后，长期从事生物统计、金融统计、因果分析及稳健统计领域前沿研究。现担任中国因果推断分会常务理事；中国工业统计学教学研究会副会长；国际生物统计学会（International）中国分会常务理事，北京大数据协会副会长等。主持科技部重点研发课题1项，1项国家自然科学重点子课题和多项国家自科面上项目等，在Annals of Statistics, Biometrika, Statistica Sinica等顶尖期刊发表学术论文50余篇。