In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
Sampling from a truncated multivariate normal distribution （TMVND） constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data au...Sampling from a truncated multivariate normal distribution （TMVND） constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation （DA） algorithm and a non-iterative inverse Bayes formulae （IBF） sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA Mgorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and elimi- nares problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.展开更多
In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased est...In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.展开更多
Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and varianc...Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.展开更多
This paper investigates and discusses the use of information divergence,through the widely used Kullback–Leibler(KL)divergence,under the multivariate(generalized)γ-order normal distribution(γ-GND).The behavior of t...This paper investigates and discusses the use of information divergence,through the widely used Kullback–Leibler(KL)divergence,under the multivariate(generalized)γ-order normal distribution(γ-GND).The behavior of the KL divergence,as far as its symmetricity is concerned,is studied by calculating the divergence of γ-GND over the Student’s multivariate t-distribution and vice versa.Certain special cases are also given and discussed.Furthermore,three symmetrized forms of the KL divergence,i.e.,the Jeffreys distance,the geometric-KL as well as the harmonic-KL distances,are computed between two members of the γ-GND family,while the corresponding differences between those information distances are also discussed.展开更多
文摘In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
基金Supported by the National Social Science Foundation of China (No. 09BTJ012)Scientific Research Fund ofHunan Provincial Education Department (No. 09c390)+1 种基金supported in part by a HKUSeed Funding Program for Basic Research (Project No. 2009-1115-9042)a grant from Hong Kong ResearchGrant Council-General Research Fund (Project No. HKU779210M)
文摘Sampling from a truncated multivariate normal distribution （TMVND） constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation （DA） algorithm and a non-iterative inverse Bayes formulae （IBF） sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA Mgorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and elimi- nares problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11201452 and 11271346)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402120017)the Fundamental Research Funds for the Central Universities(Grant No.WK0010000052)
文摘In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.
文摘Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.
文摘This paper investigates and discusses the use of information divergence,through the widely used Kullback–Leibler(KL)divergence,under the multivariate(generalized)γ-order normal distribution(γ-GND).The behavior of the KL divergence,as far as its symmetricity is concerned,is studied by calculating the divergence of γ-GND over the Student’s multivariate t-distribution and vice versa.Certain special cases are also given and discussed.Furthermore,three symmetrized forms of the KL divergence,i.e.,the Jeffreys distance,the geometric-KL as well as the harmonic-KL distances,are computed between two members of the γ-GND family,while the corresponding differences between those information distances are also discussed.
