上海财经大学统计与管理学院：以应用型II多元t分布

　　上海财经大学统计与管理学院邀请田国梁教授作了一场题为“A new robust regression model: Type II multivariate t distribution with applications(一个新的强大的回归模型：以应用型II多元t分布)”的讲座。统计与管理学院主要的学科专业是统计学，包括经济管理统计、金融统计、统计理论与方法、数量金融与风险管理等多个学科方向。上海财经大学统计学科是一个历史悠久、成绩斐然的学科。讲座的主要内容是：

　　通过实际数据分析的启发，我们在本文中通过随机代表性，而不是联合密度函数提出了新的多元t(MVT)分布。这项新的经销称为II型MVT分布，具有几个显着的特点包括：(1)所有部件遵循单变量的T分布有不同程度的自由;(2)它可以包括下列多元正态分布组件时，相应的自由度方法为无穷大，和(3)它可以包含独立/不相关的部件。由于避免了与传统的MVT分布相关的三个缺点，这种新的分布是型号规格更灵活，适用于任何高维数据。重要的分布性质进行了探索和有益的统计方法的开发。模拟研究，以评估所提出的方法。两个生物医学数据集用于比较与传统MVT分配所提出的II型MVT分布。 (这是张驰小姐的联合工作)

　　原文：Motivated by a real data analysis, we in this paper propose a new multivariate t (MVT) distribution via stochastic representation instead of the joint density function. This new distribution is called Type II MVT distribution, which possesses several remarkable features including (1) all components follow univariate t-distributions with different degrees of freedom, (2) it could include components following the multivariate normal distributions when the corresponding degrees of freedom approach to infinity, and (3) it could contain independent/uncorrelated components. Because of avoiding three drawbacks associated with the traditional MVT distribution, this new distribution is more flexible in model specification and applicable to any highdimensional data. Important distributional properties are explored and useful statistical methods are developed. Simulation studies are performed to evaluate the proposed methods. Two biomedical data sets are used to compare the proposed Type II MVT distribution with the traditional MVT distribution. (This is a joint work with Miss Chi ZHANG)