走向现代数学学术报告 - 施建华教授（No. 686）

题目：Mean regression model for the zero-truncated Poisson distribution and its generalization

报告人：施建华 教授（闽南师范大学）

时间：2024年1月16日 16:00

地点：东海岸校区-D209

摘要：Zero-truncated count data often arise in various fields such as medical studies. To model such data, the zero-truncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients β or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of β. This work aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of a challenge that the original Poisson mean parameter λi cannot be expressed explicitly by the ZTP mean parameter μi , an embedded Newton–Raphson algorithm is developed to calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the k-truncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods.

报告人简介：施建华，教授，硕士生导师。2015年毕业于上海财经大学，获经济学博士学位。曾担任数学与统计学院副院长，目前担任福建省粒计算及其应用重点实验室副主任，兼任漳州市统计学会会长、全国青年统计学家协会常务理事等职。主要从事统计学、数学相关领域的教学与研究。已在《Computational Statistics and Data Analysis》、《Statistics & Probability Letters》、《SCIENCE CHINA Mathematics(English series)》等国内外学术期刊上发表三十余篇学术论文。先后主持完成福建省自然科学基金项目、福建省级教改项目等多项课题，目前主持国家社会科学基金项目一项，获军事科学技术进步奖二等奖一项。