In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance m...In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be...A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be efficiently analysed by a finite mixture of regression models.These observations motivate us to propose a novel finite mixture of median regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several subpopulations.With the appropriate choice of the tuning parameters,we establish the theoretical properties of the proposed procedure,including consistency for variable selection method and the oracle property in estimation.A productive nonparametric clustering method is applied to select the number of components,and an efficient EM algorithm for numerical computations is developed.Simulation studies and a real data set are used to illustrate the performance of the proposed methodologies.展开更多
Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effect...Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.展开更多
文摘In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.
基金the National Natural Science Foundation of China[grant number 11861041]the Natural Science Research Foundation of Kunming University of Science and Technology[grant number KKSY201907003].
文摘A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes.Moreover,data that arise from a heterogeneous population can be efficiently analysed by a finite mixture of regression models.These observations motivate us to propose a novel finite mixture of median regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several subpopulations.With the appropriate choice of the tuning parameters,we establish the theoretical properties of the proposed procedure,including consistency for variable selection method and the oracle property in estimation.A productive nonparametric clustering method is applied to select the number of components,and an efficient EM algorithm for numerical computations is developed.Simulation studies and a real data set are used to illustrate the performance of the proposed methodologies.
基金Dr.Wu was supported by the National Natural Science Foundation of China under grant 11861041Drs.Keying Ye and Min Wang were partially supported by a grant from the UTSA Vice President for Research,Economic Development,and Knowledge Enterprise at the University of Texas at San Antonio.
文摘Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.