A new multivariate t distribution with variant tail weights and its application in robust regression analysis

Chi Zhang; Guo-Liang Tian; Kam Chuen Yuen; Pengyi Liu; Man-Lai Tang

doi:10.1080/02664763.2021.1913106

A new multivariate t distribution with variant tail weights and its application in robust regression analysis

J Appl Stat. 2021 Apr 14;49(10):2629-2656. doi: 10.1080/02664763.2021.1913106. eCollection 2022.

Authors

Chi Zhang¹, Guo-Liang Tian², Kam Chuen Yuen³, Pengyi Liu⁴, Man-Lai Tang⁵

Affiliations

¹ College of Economics, Shenzhen University, Shenzhen, Guangdong Province, People's Republic of China.
² Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, Guangdong Province, People's Republic of China.
³ Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, People's Republic of China.
⁴ School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan Province, People's Republic of China.
⁵ Department of Mathematics, Statistics and Insurance, School of Decision Sciences, The Hang Seng University of Hong Kong, Hong Kong, People's Republic of China.

Abstract

In this paper, we propose a new kind of multivariate t distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate t distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent t-distributions as a special case. Subsequently, it is extended to the regression model as the joint distribution of the error terms. Important distributional properties are explored and useful statistical methods are developed. The flexibility of the specified structure in better capturing the characteristic of data is exemplified by both simulation studies and real data analyses.

Keywords: Expectation/conditional maximization algorithm; multivariate t distribution; multivariate t regression model; multivariate truncated normal distribution; stochastic representation.

Grants and funding

Chi Zhang's research was supported by National Natural Science Foundation of China (Grant No. 11801380). Guo-Liang Tian's research was fully supported by National Natural Science Foundation of China (Grant No. 11771199). Kam Chuen Yuen's research was supported by a Seed Fund for Basic Research of the University of Hong Kong, and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU17306220). The work of Man-Lai Tang was partially supported through grants from the Research Grant Council of the Hong Kong Special Administrative Region (UGC/FDS14/P06/17, UGC/FDS14/P02/18, and the Research Matching Grant Scheme (RMGS)) and a grant from the National Natural Science Foundation of China (11871124). The computing facilities/software were supported by SAS Viya and the Big Data Intelligence Centre at Hang Seng University of Hong Kong.