报告题目：A class of new symmetric distributions based on scale mixtures of normal distribution and mean regression models by using N-EM and US algorithms

报告人：田国梁

时间：4月25日 14：00-14：50

地点：体育赛事直播平台 106会议室

报告摘要：In this paper, we propose a class of new symmetric distributions as candidates or alternatives to model continuous data on the real line, when existing distributions (such as normal, Student's t, two-parameter Laplace, logistic and so on) perform the data-fitting not well enough. Motivated by the stochastic representation (SR) of the random variable (r.v.) following Student's t-distribution, the authors study the general mixture of normal (Ge-N) distribution, which is defined by an SR involving a normal r.v. with zero mean and a positive r.v. with an arbitrary distribution. The Ge-N distribution includes the commonly-used t, two-parameter Laplace, logistic distributions as three special cases and possesses a clear statistical interpretation. In the Ge-N framework, we first address the issue of identifiability of parameters, then develop three specific scale mixtures of normal distribution and corresponding mean regression models for analyzing continuous data with covariates. We apply the normalized expectation-maximization (N-EM) algorithm aided by the upper-crossing/solution (US) algorithm to calculate maximum likelihood estimates of parameters. Simulation studies on model comparisons showed that the proposed three new models extend the application scope of existing models. Two real data sets are analyzed to illustrate the proposed methods.[This is a joint work with Mr. Yuefan WU,  Mr. Yuanfan ZHAO, Prof. Zudi LU, Dr. Xun-Jian LI]

报告人简介：田国梁，南方科技大学统计与数据科学系教授，曾在美国马里兰大学从事医学统计研究六年, 在香港大学统计与精算学系任副教授八年, 从 2016 年 6 月至今在南方科技大学统计与数据科学系任教授、博士生导师。他目前的研究方向为 EM/MM/US 算法在统计中的应用、(0, 1) 区间上连续比例数据以及多元连续比例数据的统计分析、连续对称和连续非对称数据分析, 在国外发表 160 余篇 SCI 论文、出版 3 本英文专著、在科学出版社出版英文教材 2 本。他曾是四个国际统计期刊的副主编, 目前是国际统计期刊 SII (Statistics and Its Interface) 的副主编。主持国家自然科学基金面上项目二项、主持深圳市稳定支持面上项目一项、参加国家自然科学基金重点项目一项。