{"title":"截断Student-t回归模型的有效性质及其在截尾数据分析中的应用","authors":"Chi Zhang, Guozheng Tian, Yibo Zhai, Y. Fei","doi":"10.1214/21-bjps521","DOIUrl":null,"url":null,"abstract":"Kim (2008) 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 (2008), 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.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Valid properties of truncated Student-t regression model with applications in analysis of censored data\",\"authors\":\"Chi Zhang, Guozheng Tian, Yibo Zhai, Y. Fei\",\"doi\":\"10.1214/21-bjps521\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Kim (2008) 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 (2008), 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.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/21-bjps521\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps521","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Valid properties of truncated Student-t regression model with applications in analysis of censored data
Kim (2008) 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 (2008), 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.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.