Title of the Talk:

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

(基于正态分布的尺度混合的一类新的对称分布及均值回归模型:用N-EM和US算法来计算其参数的MLEs)

时间：2026年4月14日(周二)下午16：00 -17：30 地点：H313

Speaker:

Guo-Liang TIAN, Professor of Statistics

Department of Statistics and Data Science,

Southern University of Science and Technology

中文摘要:

当现有的分布（如正态分布、t分布、双参数拉普拉斯分布、logistic分布等）对连续数据拟合不满意时，本文所提出的一类新的对称分布可以作为拟合实数线上连续数据的候选分布或替代分布。受服从学生t分布的随机变量之随机表示（Stochastic Representation, SR）的启发，本文作者研究了正态分布的一般混合（General Mixture of Normal, Ge-N），该分布由SR所定义，它涉及到带零均值的正态随机变量和服从任意分布的正随机变量。Ge-N分布包括常用的学生t、双参数拉普拉斯、logistic分布作为三种特例，并且Ge-N随机变量之SR具有清晰的统计解释。在Ge-N框架中，我们首先解决了参数的可识别性问题，其次研究了三个特殊的正态分布的尺度混合(Scale Mixtures of Normal Distribution)和相应的均值回归模型，用于分析具有协变量的连续型数据。我们采用正则期望最大化（Normalized Expectation-Maximization, N-EM）算法，辅以上交叉/求解（Upper-crossing/Solution, US）算法来计算参数的最大似然估计。模拟研究和实例分析结果表明，提出的三种新模型拓展了现有模型的应用范围.

English Abstract:

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'st, two-parameter Laplace, logistic and so on) perform the data-fitting not well enough. Motivated by thestochastic representation (SR) of therandom variable (r.v.) following Student'st-distribution, the authors study thegeneral mixture of normal(Ge-N) distribution, which is defined by an SR involving a normal r.v. with zero mean and a positiver.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 thenormalized expectation-maximization (N-EM) algorithm aided by theupper-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]

主讲人介绍：田国梁博士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。

Dr. Guoliang Tian has been engaged in medical statistics research at the University of Maryland at Baltimore for six years, and served as an Associate Professor in the Department of Statistics and Actuarial Science at the University of Hong Kong for eight years. From June 2016 to present, he has been a Full Professor at the Department of Statistics and Data Science in Southern University of Science and Technology. His current research directions include the application of EM/MM/US/SeLF algorithms in statistics, statistical analysis of continuous proportional data on (0,1) intervals and multivariate continuous proportional data, & continuous symmetrical and asymmetrical data analysis. He has published over 150 SCI papers, 3 English monographs, and 2 English textbooks published by Science Press. He was the AE of four international statistical journals and is currently the AE of the SII (Statistics and Its Interface). Hosted two National Natural Science Foundation general projects, and participated in one National Natural Science Foundation key project.