Pub Date : 2021-12-16DOI: 10.1080/24754269.2021.2015861
Junlong Zhao
Distributed statistical inferences have attracted more and more attention in recent years with the emergence of massive data. We are grateful to the authors for the excellent review of the literature in this active area. Besides the progress mentioned by the authors, we would like to discuss some additional development in this interesting area. Specifically, we focus on the balance of communication cost and the statistical efficiency of divide-and-conquer (DC) type estimators in linear discriminant analysis and hypothesis testing. It is seen that the DC approach has different behaviours in these problems, which is different from that in estimation problems. Furthermore, we discuss some issues on the statistical inferences under restricted communication budgets.
{"title":"Discussion on the paper ‘A review of distributed statistical inference’","authors":"Junlong Zhao","doi":"10.1080/24754269.2021.2015861","DOIUrl":"https://doi.org/10.1080/24754269.2021.2015861","url":null,"abstract":"Distributed statistical inferences have attracted more and more attention in recent years with the emergence of massive data. We are grateful to the authors for the excellent review of the literature in this active area. Besides the progress mentioned by the authors, we would like to discuss some additional development in this interesting area. Specifically, we focus on the balance of communication cost and the statistical efficiency of divide-and-conquer (DC) type estimators in linear discriminant analysis and hypothesis testing. It is seen that the DC approach has different behaviours in these problems, which is different from that in estimation problems. Furthermore, we discuss some issues on the statistical inferences under restricted communication budgets.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"108 - 110"},"PeriodicalIF":0.5,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46176137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1080/24754269.2021.1991557
Ying-Ying Zhang, Tengzhong Rong, Man-Man Li
ABSTRACT When the historical data of the early phase trial and the interim data of the Phase III trial are available, we should use them to give a more accurate prediction in both futility and efficacy analysis. The predictive power is an important measure of the practical utility of a proposed trial, and it is better than the classical statistical power in giving a good indication of the probability that the trial will demonstrate a positive or statistically significant outcome. In addition to the four predictive powers with historical and interim data available in the literature and summarized in Table 1, we discover and calculate another four predictive powers also summarized in Table 1, for one-sided hypotheses. Moreover, we calculate eight predictive powers summarized in Table 2, for the reversed hypotheses. The combination of the two tables gives us a complete picture of the predictive powers with historical and interim data for futility and efficacy analysis. Furthermore, the eight predictive powers with historical and interim data are utilized to guide the futility analysis in the tamoxifen example. Finally, extensive simulations have been conducted to investigate the sensitivity analysis of priors, sample sizes, interim result and interim time on different predictive powers.
{"title":"Eight predictive powers with historical and interim data for futility and efficacy analysis","authors":"Ying-Ying Zhang, Tengzhong Rong, Man-Man Li","doi":"10.1080/24754269.2021.1991557","DOIUrl":"https://doi.org/10.1080/24754269.2021.1991557","url":null,"abstract":"ABSTRACT When the historical data of the early phase trial and the interim data of the Phase III trial are available, we should use them to give a more accurate prediction in both futility and efficacy analysis. The predictive power is an important measure of the practical utility of a proposed trial, and it is better than the classical statistical power in giving a good indication of the probability that the trial will demonstrate a positive or statistically significant outcome. In addition to the four predictive powers with historical and interim data available in the literature and summarized in Table 1, we discover and calculate another four predictive powers also summarized in Table 1, for one-sided hypotheses. Moreover, we calculate eight predictive powers summarized in Table 2, for the reversed hypotheses. The combination of the two tables gives us a complete picture of the predictive powers with historical and interim data for futility and efficacy analysis. Furthermore, the eight predictive powers with historical and interim data are utilized to guide the futility analysis in the tamoxifen example. Finally, extensive simulations have been conducted to investigate the sensitivity analysis of priors, sample sizes, interim result and interim time on different predictive powers.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"277 - 298"},"PeriodicalIF":0.5,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49302617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1080/24754269.2021.1984373
Long Feng, Xiaoxu Zhang, Binghui Liu
With the development of modern science and technology, more and more high-dimensional data appear in the application fields. Since the high dimension can potentially increase the complexity of the covariance structure, comparing the covariance matrices among populations is strongly motivated in high-dimensional data analysis. In this article, we consider the proportionality test of two high-dimensional covariance matrices, where the data dimension is potentially much larger than the sample sizes, or even larger than the squares of the sample sizes. We devise a novel high-dimensional spatial rank test that has much-improved power than many existing popular tests, especially for the data generated from some heavy-tailed distributions. The asymptotic normality of the proposed test statistics is established under the family of elliptically symmetric distributions, which is a more general distribution family than the normal distribution family, including numerous commonly used heavy-tailed distributions. Extensive numerical experiments demonstrate the superiority of the proposed test in terms of both empirical size and power. Then, a real data analysis demonstrates the practicability of the proposed test for high-dimensional gene expression data.
{"title":"High-dimensional proportionality test of two covariance matrices and its application to gene expression data","authors":"Long Feng, Xiaoxu Zhang, Binghui Liu","doi":"10.1080/24754269.2021.1984373","DOIUrl":"https://doi.org/10.1080/24754269.2021.1984373","url":null,"abstract":"With the development of modern science and technology, more and more high-dimensional data appear in the application fields. Since the high dimension can potentially increase the complexity of the covariance structure, comparing the covariance matrices among populations is strongly motivated in high-dimensional data analysis. In this article, we consider the proportionality test of two high-dimensional covariance matrices, where the data dimension is potentially much larger than the sample sizes, or even larger than the squares of the sample sizes. We devise a novel high-dimensional spatial rank test that has much-improved power than many existing popular tests, especially for the data generated from some heavy-tailed distributions. The asymptotic normality of the proposed test statistics is established under the family of elliptically symmetric distributions, which is a more general distribution family than the normal distribution family, including numerous commonly used heavy-tailed distributions. Extensive numerical experiments demonstrate the superiority of the proposed test in terms of both empirical size and power. Then, a real data analysis demonstrates the practicability of the proposed test for high-dimensional gene expression data.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"161 - 174"},"PeriodicalIF":0.5,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43264799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1080/24754269.2021.1982607
Shiferaw B. Bizuayehu, Luquan Li, Jin Xu
We propose two variable selection methods in multivariate linear regression with high-dimensional covariates. The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level. The second method extends the univariate forward regression of Wang [(2009). Forward regression for ultra-high dimensional variable screening. Journal of the American Statistical Association, 104(488), 1512–1524. https://doi.org/10.1198/jasa.2008.tm08516] in a unified way such that the variable selection and model estimation can be obtained simultaneously. We establish the sure screening property for both methods. Simulation and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.
{"title":"Variable screening in multivariate linear regression with high-dimensional covariates","authors":"Shiferaw B. Bizuayehu, Luquan Li, Jin Xu","doi":"10.1080/24754269.2021.1982607","DOIUrl":"https://doi.org/10.1080/24754269.2021.1982607","url":null,"abstract":"We propose two variable selection methods in multivariate linear regression with high-dimensional covariates. The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level. The second method extends the univariate forward regression of Wang [(2009). Forward regression for ultra-high dimensional variable screening. Journal of the American Statistical Association, 104(488), 1512–1524. https://doi.org/10.1198/jasa.2008.tm08516] in a unified way such that the variable selection and model estimation can be obtained simultaneously. We establish the sure screening property for both methods. Simulation and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"241 - 253"},"PeriodicalIF":0.5,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47622019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-26DOI: 10.1080/24754269.2021.1980261
Fariha Sohil, Muhammad Umair Sohali, J. Shabbir
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. This textbook considers statistical learning applications when interest centers on the conditional distribution of a response variable, given a set of predictors, and in the absence of a credible model that can be specified before the data analysis begins. Consistent with modern data analytics, it emphasizes that a proper statistical learning data analysis depends in an integrated fashion on sound data collection, intelligent data management, appropriate statistical procedures, and an
{"title":"An introduction to statistical learning with applications in R","authors":"Fariha Sohil, Muhammad Umair Sohali, J. Shabbir","doi":"10.1080/24754269.2021.1980261","DOIUrl":"https://doi.org/10.1080/24754269.2021.1980261","url":null,"abstract":"The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. This textbook considers statistical learning applications when interest centers on the conditional distribution of a response variable, given a set of predictors, and in the absence of a credible model that can be specified before the data analysis begins. Consistent with modern data analytics, it emphasizes that a proper statistical learning data analysis depends in an integrated fashion on sound data collection, intelligent data management, appropriate statistical procedures, and an","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"87 - 87"},"PeriodicalIF":0.5,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42115335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-23DOI: 10.1080/24754269.2021.1978207
Xiuzhen Zhang, Yukun Liu, Riquan Zhang, Zhiping Lu
Depending on the asymptotical independence of periodograms, exponential tilted (ET) likelihood, as an effective nonparametric statistical method, is developed to deal with time series in this paper. Similar to empirical likelihood (EL), it still suffers from two drawbacks: the non-definition problem of the likelihood function and the under-coverage probability of confidence region. To overcome these two problems, we further proposed the adjusted ET (AET) likelihood. With a specific adjustment level, our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method. In addition, due to the good performance of ET under moment model misspecification [Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. The Annals of Statistics, 35(2), 634–672. https://doi.org/10.1214/009053606000001208], we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1). The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation. A real data set is analyzed for illustration purpose.
{"title":"Exponential tilted likelihood for stationary time series models","authors":"Xiuzhen Zhang, Yukun Liu, Riquan Zhang, Zhiping Lu","doi":"10.1080/24754269.2021.1978207","DOIUrl":"https://doi.org/10.1080/24754269.2021.1978207","url":null,"abstract":"Depending on the asymptotical independence of periodograms, exponential tilted (ET) likelihood, as an effective nonparametric statistical method, is developed to deal with time series in this paper. Similar to empirical likelihood (EL), it still suffers from two drawbacks: the non-definition problem of the likelihood function and the under-coverage probability of confidence region. To overcome these two problems, we further proposed the adjusted ET (AET) likelihood. With a specific adjustment level, our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method. In addition, due to the good performance of ET under moment model misspecification [Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. The Annals of Statistics, 35(2), 634–672. https://doi.org/10.1214/009053606000001208], we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1). The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation. A real data set is analyzed for illustration purpose.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"254 - 263"},"PeriodicalIF":0.5,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44094075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-13DOI: 10.1080/24754269.2021.1971489
Gökhan Gökdere, H. K. Tony Ng
In a repairable consecutive system, after the system operates for a certain time, some components may fail, some failed components may be repaired and the state of the system may change. The models developed in the existing literature usually assume that the state of the system varies over time depending on the values of n and k and the state of the system is known. Since the system reliability will vary over time, it is of great interest to analyse the time-dependent system reliability. In this paper, we develop a novel and simple method that utilizes the eigenvalues of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known. In addition, the transition performance probabilities of the system from a known state to the possible states are also analysed. Computational results are presented to illustrate the applicability and accuracy of the proposed method.
{"title":"Time-dependent reliability analysis for repairable consecutive-k-out-of-n:F system","authors":"Gökhan Gökdere, H. K. Tony Ng","doi":"10.1080/24754269.2021.1971489","DOIUrl":"https://doi.org/10.1080/24754269.2021.1971489","url":null,"abstract":"In a repairable consecutive system, after the system operates for a certain time, some components may fail, some failed components may be repaired and the state of the system may change. The models developed in the existing literature usually assume that the state of the system varies over time depending on the values of n and k and the state of the system is known. Since the system reliability will vary over time, it is of great interest to analyse the time-dependent system reliability. In this paper, we develop a novel and simple method that utilizes the eigenvalues of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known. In addition, the transition performance probabilities of the system from a known state to the possible states are also analysed. Computational results are presented to illustrate the applicability and accuracy of the proposed method.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"139 - 147"},"PeriodicalIF":0.5,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44643166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of divide-and-conquer, various distributed frameworks for statistical estimation and inference have been proposed. They were developed to deal with large-scale statistical optimization problems. This paper aims to provide a comprehensive review for related literature. It includes parametric models, nonparametric models, and other frequently used models. Their key ideas and theoretical properties are summarized. The trade-off between communication cost and estimate precision together with other concerns is discussed.
{"title":"A review of distributed statistical inference","authors":"Yuan Gao, Weidong Liu, Hansheng Wang, Xiaozhou Wang, Yibo Yan, Riquan Zhang","doi":"10.1080/24754269.2021.1974158","DOIUrl":"https://doi.org/10.1080/24754269.2021.1974158","url":null,"abstract":"The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of divide-and-conquer, various distributed frameworks for statistical estimation and inference have been proposed. They were developed to deal with large-scale statistical optimization problems. This paper aims to provide a comprehensive review for related literature. It includes parametric models, nonparametric models, and other frequently used models. Their key ideas and theoretical properties are summarized. The trade-off between communication cost and estimate precision together with other concerns is discussed.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"89 - 99"},"PeriodicalIF":0.5,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46736414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-08DOI: 10.1080/24754269.2021.1974157
Tri Le, B. Clarke
Many of the best predictors for complex problems are typically regarded as hard to interpret physically. These include kernel methods, Shtarkov solutions, and random forests. We show that, despite the inability to interpret these three predictors to infinite precision, they can be asymptotically approximated and admit conceptual interpretations in terms of their mathematical/statistical properties. The resulting expressions can be in terms of polynomials, basis elements, or other functions that an analyst may regard as interpretable.
{"title":"Interpreting uninterpretable predictors: kernel methods, Shtarkov solutions, and random forests","authors":"Tri Le, B. Clarke","doi":"10.1080/24754269.2021.1974157","DOIUrl":"https://doi.org/10.1080/24754269.2021.1974157","url":null,"abstract":"Many of the best predictors for complex problems are typically regarded as hard to interpret physically. These include kernel methods, Shtarkov solutions, and random forests. We show that, despite the inability to interpret these three predictors to infinite precision, they can be asymptotically approximated and admit conceptual interpretations in terms of their mathematical/statistical properties. The resulting expressions can be in terms of polynomials, basis elements, or other functions that an analyst may regard as interpretable.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"10 - 28"},"PeriodicalIF":0.5,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46715213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-05DOI: 10.1080/24754269.2021.1963182
Xuan Cao, F. Yang
We consider sparsity selection for the Cholesky factor L of the inverse covariance matrix in high-dimensional Gaussian DAG models. The sparsity is induced over the space of L via non-local priors, namely the product moment (pMOM) prior [Johnson, V., & Rossell, D. (2012). Bayesian model selection in high-dimensional settings. Journal of the American Statistical Association, 107(498), 649–660. https://doi.org/10.1080/01621459.2012.682536] and the hierarchical hyper-pMOM prior [Cao, X., Khare, K., & Ghosh, M. (2020). High-dimensional posterior consistency for hierarchical non-local priors in regression. Bayesian Analysis, 15(1), 241–262. https://doi.org/10.1214/19-BA1154]. We establish model selection consistency for Cholesky factor under more relaxed conditions compared to those in the literature and implement an efficient MCMC algorithm for parallel selecting the sparsity pattern for each column of L. We demonstrate the validity of our theoretical results via numerical simulations, and also use further simulations to demonstrate that our sparsity selection approach is competitive with existing methods.
{"title":"On the non-local priors for sparsity selection in high-dimensional Gaussian DAG models","authors":"Xuan Cao, F. Yang","doi":"10.1080/24754269.2021.1963182","DOIUrl":"https://doi.org/10.1080/24754269.2021.1963182","url":null,"abstract":"We consider sparsity selection for the Cholesky factor L of the inverse covariance matrix in high-dimensional Gaussian DAG models. The sparsity is induced over the space of L via non-local priors, namely the product moment (pMOM) prior [Johnson, V., & Rossell, D. (2012). Bayesian model selection in high-dimensional settings. Journal of the American Statistical Association, 107(498), 649–660. https://doi.org/10.1080/01621459.2012.682536] and the hierarchical hyper-pMOM prior [Cao, X., Khare, K., & Ghosh, M. (2020). High-dimensional posterior consistency for hierarchical non-local priors in regression. Bayesian Analysis, 15(1), 241–262. https://doi.org/10.1214/19-BA1154]. We establish model selection consistency for Cholesky factor under more relaxed conditions compared to those in the literature and implement an efficient MCMC algorithm for parallel selecting the sparsity pattern for each column of L. We demonstrate the validity of our theoretical results via numerical simulations, and also use further simulations to demonstrate that our sparsity selection approach is competitive with existing methods.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"332 - 345"},"PeriodicalIF":0.5,"publicationDate":"2021-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47443670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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