A new robust regression model: Type II multivariate t distribution with applications
Speaker:Prof. Guo-Liang TIAN
Associate Professor
Department of Statistics and Actuarial Science
The University of Hong Kong
Hong Kong
Date & Time:6 May 2016 (Friday) 10:30 - 11:30
Venue:E11-1040
Organized by:Department of Mathematics

Abstract

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 high- dimensional 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)

Biography

Guo-Liang Tian, Ph.D., is an Associate Professor of Statistics at Department of Statistics and Actuarial Science, The University of Hong Kong, where he teaches computational statistics, statistical models and multivariate methods. He was a faculty bio-statistician at the University of Maryland Greenebaum Cancer Center (Baltimore, Maryland, USA) from 2002 to 2008, a Postdoctoral Research Associate at Department of Biostatistics, St. Jude Children's Research Hospital (Memphis, Tennessee, USA) from 2000 to 2002, and a Postdoctoral Fellowship at Department of Probability and Statistics, Peking University (Beijing, P.R. China) from 1998 to 2000. He earned his Ph.D. in statistics in 1998 from the Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing. He was an Elected Member of International Statistics Institute, an Associate Editor of four statistical journals (Computational Statistics and Data Analysis, Statistics and Its Interface; Communications in Statistics - Theory and Methods; Communications in Statistics - Simulation and Computation). His current research interests include multivariate zero-inflated count data analysis, incomplete categorical data analysis and sample surveys with sensitive questions. He was the author of over 85 (bio)-statistical and medical articles in peer-reviewed international academic journals. He has three monographs:

  1. Tan M, Tian GL and Ng KW (2010). Bayesian Missing Data Problems: EM, Data Augmentation and Non-iterative Computation. Chapman & Hall/CRC (Biostatistics Series), Boca Raton, USA.
  2. Ng KW, Tian GL and Tang ML (2011). Dirichlet and Related Distributions: Theory, Methods and Applications. John Wiley & Sons (Wiley Series in Probability and Statistics), New York, USA.
  3. Tian GL and Tang ML (2014). Incomplete Categorical Data Design: Non-randomized Response Techniques for Sensitive Questions in Surveys.  Chapman & Hall/CRC (Statistics in the Social and Behavioral Sciences), Boca Raton, USA.