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

Zhang，Chi1; Tian，Guo Liang2; Yuen，Kam Chuen3; Liu，Pengyi4; Tang，Man Lai5

2021

10.1080/02664763.2021.1913106

JOURNAL OF APPLIED STATISTICS   影响因子和分区

0266-4763

1360-0532

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.

Expectation/conditional maximization algorithm multivariate t distribution multivariate t regression model multivariate truncated normal distribution stochastic representation

SCI

英语

其他

National Natural Science Foundation of China[11801380,11771199,11871124] ; Research Grants Council of the Hong Kong Special Administrative Region, China[HKU17306220] ; Research Grant Council of the Hong Kong Special Administrative Region["UGC/FDS14/P06/17","UGC/FDS14/P02/18"]

Mathematics

Statistics & Probability

WOS:000640172300001

TAYLOR & FRANCIS LTD

MATHEMATICS

2-s2.0-85104379521

Scopus

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

Zhang，Chi,Tian，Guo Liang,Yuen，Kam Chuen,et al. A new multivariate t distribution with variant tail weights and its application in robust regression analysis[J]. JOURNAL OF APPLIED STATISTICS,2021.

Zhang，Chi,Tian，Guo Liang,Yuen，Kam Chuen,Liu，Pengyi,&Tang，Man Lai.(2021).A new multivariate t distribution with variant tail weights and its application in robust regression analysis.JOURNAL OF APPLIED STATISTICS.

Zhang，Chi,et al."A new multivariate t distribution with variant tail weights and its application in robust regression analysis".JOURNAL OF APPLIED STATISTICS (2021).