Abstract
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.
Funding Statement
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 and 12171225). Yu Fei’s research was fully supported by National Natural Science Foundation of China (Grant no. 11971421) and Yunling Scholar Research Fund of Yunnan Province (YNWR-YLXZ-2018-020).
Acknowledgments
The authors are grateful to the Editor and three anonymous referees’ valuable comments and suggestions for significant improvements of the paper.
Chi Zhang and Guo-Liang Tian contributed equally.
Citation
Chi Zhang. Guo-Liang Tian. Yibo Zhai. Yu Fei. "Valid properties of truncated Student-t regression model with applications in analysis of censored data." Braz. J. Probab. Stat. 36 (1) 157 - 184, March 2022. https://doi.org/10.1214/21-BJPS521
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