Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empir...Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.展开更多
Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and exp...Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.展开更多
文摘Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.
基金supported by the National Natural Science Foundation of China under Grant No.11165016
文摘Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.
