Pub Date : 2023-11-07DOI: 10.1080/00949655.2023.2277339
Yuta Kurose
AbstractAn efficient random variable generator for a truncated gamma distribution with shape parameter greater than 1 is designed using an acceptance-rejection algorithm. Based on an approximation to a transformed gamma density function by the standard normal density, numerical information for the standard normal density is prepared in advance, and the calculation is performed with reference to that information. An improvement via a squeezing method is proposed to reduce the computational burden and time. The algorithm's acceptance rate for generating truncated gamma variables is very high and almost 1 when the truncated distribution is unimodal. Numerical experiments for one- and two-sided truncated domain cases are conducted to measure the execution time, including the parameter setup time. Compared with existing truncated gamma variate generators, the proposed method performs better when the distribution is unimodal and the shape parameter is equal to or greater than 3.3.Keywords: Acceptance-rejection algorithmshape parametersqueezingtruncated gamma distributionMathematics Subject Classifications: 65C0565C1062-08 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by JSPS KAKENHI Grant Numbers JP19H00588 and JP20K19751.
{"title":"Simulation of truncated and unimodal gamma distributions","authors":"Yuta Kurose","doi":"10.1080/00949655.2023.2277339","DOIUrl":"https://doi.org/10.1080/00949655.2023.2277339","url":null,"abstract":"AbstractAn efficient random variable generator for a truncated gamma distribution with shape parameter greater than 1 is designed using an acceptance-rejection algorithm. Based on an approximation to a transformed gamma density function by the standard normal density, numerical information for the standard normal density is prepared in advance, and the calculation is performed with reference to that information. An improvement via a squeezing method is proposed to reduce the computational burden and time. The algorithm's acceptance rate for generating truncated gamma variables is very high and almost 1 when the truncated distribution is unimodal. Numerical experiments for one- and two-sided truncated domain cases are conducted to measure the execution time, including the parameter setup time. Compared with existing truncated gamma variate generators, the proposed method performs better when the distribution is unimodal and the shape parameter is equal to or greater than 3.3.Keywords: Acceptance-rejection algorithmshape parametersqueezingtruncated gamma distributionMathematics Subject Classifications: 65C0565C1062-08 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by JSPS KAKENHI Grant Numbers JP19H00588 and JP20K19751.","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1080/00949655.2023.2277331
Anita Kumari, Indranil Ghosh, Kapil Kumar
AbstractIn this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes.KEYWORDS: Power Lindley distributionprogressive censoringmulticomponent stress–strength reliabilitymaximum likelihood estimationBayesian estimation AcknowledgementsThe authors are grateful to the Editor-in-Chief, Associate Editor and the learned reviewers for their insightful and constructive comments that led to possible improvements in the earlier version of this article.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples","authors":"Anita Kumari, Indranil Ghosh, Kapil Kumar","doi":"10.1080/00949655.2023.2277331","DOIUrl":"https://doi.org/10.1080/00949655.2023.2277331","url":null,"abstract":"AbstractIn this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes.KEYWORDS: Power Lindley distributionprogressive censoringmulticomponent stress–strength reliabilitymaximum likelihood estimationBayesian estimation AcknowledgementsThe authors are grateful to the Editor-in-Chief, Associate Editor and the learned reviewers for their insightful and constructive comments that led to possible improvements in the earlier version of this article.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"299 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
AbstractThis paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes.Keywords: Bayesian inferencebootstrapgeneralized pivotal inferenceprogressive Type-II censoringproportional hazard rate model2010 Mathematic Subject classifications: 62N0162N02 AcknowledgmentsThe authors would like to thank the editor, associate editor and the anonymous reviewer for their helpful comments and suggestions, which led to the improved presentation of this article significantly.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingYichuan Zhao acknowledges the support from NSF Grant [grant number DMS-2317533] and the Simons Foundation Grant [grant number 638679].
{"title":"Statistical inference for the partial area under ROC curve for the lower truncated proportional hazard rate models based on progressive Type-II censoring","authors":"Hossein Nadeb, Javad Estabraqi, Hamzeh Torabi, Yichuan Zhao, Saeede Bafekri","doi":"10.1080/00949655.2023.2277335","DOIUrl":"https://doi.org/10.1080/00949655.2023.2277335","url":null,"abstract":"AbstractThis paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes.Keywords: Bayesian inferencebootstrapgeneralized pivotal inferenceprogressive Type-II censoringproportional hazard rate model2010 Mathematic Subject classifications: 62N0162N02 AcknowledgmentsThe authors would like to thank the editor, associate editor and the anonymous reviewer for their helpful comments and suggestions, which led to the improved presentation of this article significantly.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingYichuan Zhao acknowledges the support from NSF Grant [grant number DMS-2317533] and the Simons Foundation Grant [grant number 638679].","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"101 s3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135539507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1080/00949655.2023.2279191
Zi Miao, Lihong Wang
AbstractFor the functional linear models in which the dependent variable is functional and the predictors are scalar, robust regularization for simultaneous variable selection and regression parameter estimation is an important yet challenging issue. In this paper, we propose two types of regularized robust estimation methods. The first estimator adopts the ideas of reproducing kernel Hilbert space, least absolute deviation and group Lasso techniques. Based on the first method, the second estimator applies the pre-whitening technique and estimates the error covariance function by using functional principal component analysis. Simulation studies are conducted to examine the performance of the proposed methods in small sample sizes. The method is also applied to the Canadian weather data set, which consists of the daily average temperature and precipitation observed by 35 meteorological stations across Canada from 1960 to 1994. Numerical simulations and real data analysis show a good performance of the proposed robust methods for function-on-scalar models.Keywords: Functional regression modelsparameter estimationrobustnessvariable selection Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China [grant number 11671194].
{"title":"Robust estimation for function-on-scalar regression models","authors":"Zi Miao, Lihong Wang","doi":"10.1080/00949655.2023.2279191","DOIUrl":"https://doi.org/10.1080/00949655.2023.2279191","url":null,"abstract":"AbstractFor the functional linear models in which the dependent variable is functional and the predictors are scalar, robust regularization for simultaneous variable selection and regression parameter estimation is an important yet challenging issue. In this paper, we propose two types of regularized robust estimation methods. The first estimator adopts the ideas of reproducing kernel Hilbert space, least absolute deviation and group Lasso techniques. Based on the first method, the second estimator applies the pre-whitening technique and estimates the error covariance function by using functional principal component analysis. Simulation studies are conducted to examine the performance of the proposed methods in small sample sizes. The method is also applied to the Canadian weather data set, which consists of the daily average temperature and precipitation observed by 35 meteorological stations across Canada from 1960 to 1994. Numerical simulations and real data analysis show a good performance of the proposed robust methods for function-on-scalar models.Keywords: Functional regression modelsparameter estimationrobustnessvariable selection Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China [grant number 11671194].","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"105 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135540067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1080/00949655.2023.2275168
Bo Li
AbstractOften arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over-dispersed data fitting to the generalized linear models, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi-likelihood estimation of the regression coefficients. A new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions is presented. This approach has a close connection to the asymptotic normality of the root in general linear models that it provides a heuristic analogy for classroom presentation. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the percentile bootstrap method to estimate the quantiles as a resampling-based alternative. As will be shown, the simultaneous test based on both the approximation methods above is anti-conservative in designs with small sample sizes. We propose the simultaneous testing method using Efron's bias-corrected percentile bootstrapping procedure as an improvement. In small-sample designs, we demonstrate through the simulation study that the proposed method provides a viable alternative to the large-sample and the percentile bootstrap approximation methods. Moreover, the proposed method persists in controlling the familywise error rate in simultaneous testing for highly over-dispersed data from substantially small-sample designs, where the percentile-t bootstrap method provides a liberal test.Keywords: Simultaneous inferencequasi-likelihood functionspercentile bootstrapbias-corrected percentile bootstraprobustness of validityover-dispersion AcknowledgmentsThe author would like to thank two anonymous referees for providing insightful comments, which have helped the author improve the article. The author would like to thank Dr. Mei-Qin Chen at The Citadel for a discussion helpful to the proof of Theorem 2.2.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 The subindex i in Sections 2 and 3 is in association to the subindices i1i2i3i4 with i1=1,2,ı2=1,2,ı3=1,2,3,4, and i4=1,2,3 in Section 8.1 in order.2 The subindex i in Sections 2 and 3 is in association to the subindices i1i2 with i1=1,…,4 and i2=1,…,ni1 in Section 8.2 in order.
{"title":"An alternative derivation of weak convergence concerning quasi-likelihood estimation with a small-sample correction for simultaneous testing","authors":"Bo Li","doi":"10.1080/00949655.2023.2275168","DOIUrl":"https://doi.org/10.1080/00949655.2023.2275168","url":null,"abstract":"AbstractOften arises in counting data analysis that both violation of distributional assumption and large-scale over-dispersion substantially impair the validity of the methods for multiple comparisons. For over-dispersed data fitting to the generalized linear models, we describe the simultaneous inference method in assessing a sequence of estimable functions based on the root using the quasi-likelihood estimation of the regression coefficients. A new method for deriving the limiting distributions of the score function and the root under a list of mild regularity conditions is presented. This approach has a close connection to the asymptotic normality of the root in general linear models that it provides a heuristic analogy for classroom presentation. Hence, researchers can routinely estimate quantiles based on the limiting distribution of the root for simultaneous inference. We apply the percentile bootstrap method to estimate the quantiles as a resampling-based alternative. As will be shown, the simultaneous test based on both the approximation methods above is anti-conservative in designs with small sample sizes. We propose the simultaneous testing method using Efron's bias-corrected percentile bootstrapping procedure as an improvement. In small-sample designs, we demonstrate through the simulation study that the proposed method provides a viable alternative to the large-sample and the percentile bootstrap approximation methods. Moreover, the proposed method persists in controlling the familywise error rate in simultaneous testing for highly over-dispersed data from substantially small-sample designs, where the percentile-t bootstrap method provides a liberal test.Keywords: Simultaneous inferencequasi-likelihood functionspercentile bootstrapbias-corrected percentile bootstraprobustness of validityover-dispersion AcknowledgmentsThe author would like to thank two anonymous referees for providing insightful comments, which have helped the author improve the article. The author would like to thank Dr. Mei-Qin Chen at The Citadel for a discussion helpful to the proof of Theorem 2.2.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 The subindex i in Sections 2 and 3 is in association to the subindices i1i2i3i4 with i1=1,2,ı2=1,2,ı3=1,2,3,4, and i4=1,2,3 in Section 8.1 in order.2 The subindex i in Sections 2 and 3 is in association to the subindices i1i2 with i1=1,…,4 and i2=1,…,ni1 in Section 8.2 in order.","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"51 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1080/00949655.2023.2274915
A. D. Dabade
AbstractThe shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set.Keywords: Bayesian estimationbeta distributioncompound negative binomial distributionshared frailtygeneralized exponential distributionMCMC algorithm AcknowledgmentsThe author is thankful to the Editor and the Referees for their comments and suggestions for improvements.Disclosure statementNo potential conflict of interest was reported by the author(s).FundingAuthor hasn't received any grant for research.
{"title":"Compound negative binomial shared frailty model with random probability of susceptibility","authors":"A. D. Dabade","doi":"10.1080/00949655.2023.2274915","DOIUrl":"https://doi.org/10.1080/00949655.2023.2274915","url":null,"abstract":"AbstractThe shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set.Keywords: Bayesian estimationbeta distributioncompound negative binomial distributionshared frailtygeneralized exponential distributionMCMC algorithm AcknowledgmentsThe author is thankful to the Editor and the Referees for their comments and suggestions for improvements.Disclosure statementNo potential conflict of interest was reported by the author(s).FundingAuthor hasn't received any grant for research.","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"54 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.1080/00949655.2023.2272210
Debashis Samanta, Debasis Kundu
{"title":"On competing risk model under step-stress stage life testing","authors":"Debashis Samanta, Debasis Kundu","doi":"10.1080/00949655.2023.2272210","DOIUrl":"https://doi.org/10.1080/00949655.2023.2272210","url":null,"abstract":"","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"13 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.1080/00949655.2023.2273960
Ruizhe Jiang, Jiujun Zhang, Zhuoxi Yu
{"title":"Adaptive EWMA control chart for monitoring two-parameter exponential distribution with type-II right censored data","authors":"Ruizhe Jiang, Jiujun Zhang, Zhuoxi Yu","doi":"10.1080/00949655.2023.2273960","DOIUrl":"https://doi.org/10.1080/00949655.2023.2273960","url":null,"abstract":"","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"BME-11 1/2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.1080/00949655.2023.2273966
Wenbo Jing, Jeffrey S. Simonoff
RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate response data, by adopting the Multivariate Regression Tree method proposed by De'Ath [2002]. The Multivariate RE-EM tree method estimates a population-level single tree structure that is driven by the multiple responses simultaneously and object-level random effects for each response variable, where correlation between the response variables and between the associated random effects are each allowed. Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. We apply the Multivariate RE-EM tree to analyze a real data set that contains multidimensional nonfinancial characteristics of poverty of different countries as responses, and various potential causes of poverty as predictors.
{"title":"A regression tree method for longitudinal and clustered data with multivariate responses","authors":"Wenbo Jing, Jeffrey S. Simonoff","doi":"10.1080/00949655.2023.2273966","DOIUrl":"https://doi.org/10.1080/00949655.2023.2273966","url":null,"abstract":"RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate response data, by adopting the Multivariate Regression Tree method proposed by De'Ath [2002]. The Multivariate RE-EM tree method estimates a population-level single tree structure that is driven by the multiple responses simultaneously and object-level random effects for each response variable, where correlation between the response variables and between the associated random effects are each allowed. Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. We apply the Multivariate RE-EM tree to analyze a real data set that contains multidimensional nonfinancial characteristics of poverty of different countries as responses, and various potential causes of poverty as predictors.","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"60 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 10.1080/00949655.2023.2273369
Jie Jiang, Tian He, Lichun Wang
AbstractThis paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.Keywords: Mixed linear modelvariance componentslinear Bayes procedure AcknowledgmentsWe would like to thank the Editor and reviewers for the comments and suggestions, which have improved the presentation and quality of the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingSupported by NNSF of China (11371051)
{"title":"Bayes estimates of variance components in mixed linear model","authors":"Jie Jiang, Tian He, Lichun Wang","doi":"10.1080/00949655.2023.2273369","DOIUrl":"https://doi.org/10.1080/00949655.2023.2273369","url":null,"abstract":"AbstractThis paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.Keywords: Mixed linear modelvariance componentslinear Bayes procedure AcknowledgmentsWe would like to thank the Editor and reviewers for the comments and suggestions, which have improved the presentation and quality of the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingSupported by NNSF of China (11371051)","PeriodicalId":50040,"journal":{"name":"Journal of Statistical Computation and Simulation","volume":"17 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135316220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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