Valid properties of truncated Student-t regression model with applications in analysis of censored data

Zhang，Chi1; Tian，Guo Liang2; Zhai，Yibo2; Fei，Yu3

2022-03-01

10.1214/21-BJPS521

Brazilian Journal of Probability and Statistics   影响因子和分区

0103-0752

Kim (J. Korean Stat. Soc. 37 (2008) 81–87) introduced an incorrect stochastic representation (SR) for the truncated Student-t (Tt) random variable. By pointing out that the gamma mixture based on a truncated normal distribution actually cannot result in a true Tt distribution, in this paper, we first propose three correct SRs and then recalculate the corresponding moments of the Tt distribution. Different from those derived by following the invalid SR of Kim (J. Korean Stat. Soc. 37 (2008) 81–87), the correct moments of the Tt distribution play a crucial role in parameter estimations. Based on the third SR proposed and the correct expressions of truncated moments, expectation–maximization (EM) algorithms are developed for calculating the maximum likelihood estimates of parameters in the Tt distribution. Extensions to a Tt regression model and a t interval-censored regression model are provided as well. Simulated experiments are conducted to evaluate the performance of the proposed methods. Finally, two real data analyses corroborate the theoretical results.

EM algorithm Interval-censored regression model Stochastic representation Truncated Student-t distribution Truncated Student-t regression model

SCI

英语

其他

National Natural Science Foundation of China[11771199];National Natural Science Foundation of China[11801380];National Natural Science Foundation of China[11971421];National Natural Science Foundation of China[12171225];

WOS:000753497700008

2-s2.0-85124819867

Scopus

1.College of Economics,Shenzhen University,Shenzhen,Guangdong Province,518055,China
2.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,Guangdong Province,518055,China
3.School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming,Yunnan Province,650221,China

Zhang，Chi,Tian，Guo Liang,Zhai，Yibo,et al. Valid properties of truncated Student-t regression model with applications in analysis of censored data[J]. Brazilian Journal of Probability and Statistics,2022,36(1):157-184.

Zhang，Chi,Tian，Guo Liang,Zhai，Yibo,&Fei，Yu.(2022).Valid properties of truncated Student-t regression model with applications in analysis of censored data.Brazilian Journal of Probability and Statistics,36(1),157-184.

Zhang，Chi,et al."Valid properties of truncated Student-t regression model with applications in analysis of censored data".Brazilian Journal of Probability and Statistics 36.1(2022):157-184.