As a typical form of symbolic data, interval-valued data provides an effective framework to analyze large-scale datasets. Most existing interval regression studies focus on classical methods, while research that incorporates heteroscedasticity within the Bayesian framework remains limited. This paper extends the existing parametric method for interval-valued data to a Bayesian heteroscedastic framework, and further develops the Bayesian Heteroscedastic Parametric Method (BHPM). By explicitly modeling heteroscedasticity in the regression structure, we conduct Bayesian inference using Gibbs sampling and the Metropolis-Hastings algorithm, thus enhancing the model's interpretability and generalization performance. Both simulation studies and real-data applications demonstrate that the extended BHPM achieves superior performance over traditional methods.

In the era of big data, interval-valued data is quite common in real life and can be used to describe the uncertainty of variables. In this paper, we introduced random effects panel interval-valued data models based on the center and range method and constructed a Bayesian method for the models, including estimation and prediction. Some simulation studies indicate that the proposed Bayesian method performs well. Finally, our proposed panel interval-valued data Bayesian models were applied in forecasting of the Air Quality Index, and the experimental evaluation of actual data sets shows the advantages and the performance of our proposed models.

This paper studied panel interval-valued data models with individual fixed effects, in which the correlation within a group was considered and the group average method was used to eliminate the fixed effects. Then, we applied generalized estimation equations (GEEs) to analyze panel interval-valued data models and gave a computational algorithm to obtain the estimators. Some Monte Carlo simulations and real data analysis showed that, in contrast with the least-squares dummy-variable (LSDV) method, the proposed GEEs method has advantages in forecasting performance.

This paper proposes a variable selection method for a semiparametric varying coefficient spatial autoregressive panel model with fixed effects based on a penalized profile quasi-likelihood method, which can simultaneously select significant variables in parametric components and nonparametric components without estimating fixed effects. With an appropriate selection of the tuning parameters and some mild assumptions, the consistency of this procedure and the oracle property of the obtained estimators are established. Then, we conduct some Monte Carlo simulations to assess the finite sample performance of the proposed variable selection method, and finally, we analyze a real dataset for further illustration.

When performing Bayesian modeling on functional data, the assumption of normality is often made on the model error and thus the results may be sensitive to outliers and/or heavy tailed data. An important and good choice for solving such problems is quantile regression. Therefore, this paper introduces the quantile regression into the partial functional linear spatial autoregressive model (PFLSAM) based on the asymmetric Laplace distribution for the errors. Then, the idea of the functional principal component analysis, and the hybrid MCMC algorithm combining Gibbs sampling and the Metropolis–Hastings algorithm are developed to generate posterior samples from the full posterior distributions to obtain Bayesian estimation of unknown parameters and functional coefficients in the model. Finally, some simulation studies show that the proposed Bayesian estimation method is feasible and effective.

Achieving “dual carbon” targets by containing carbon emissions while sustaining economic growth is challenging. This study examines the varying carbon dependency levels among China’s 30 provincial-level administrative units, considering spatial correlations in emissions. Using a semi-parametric varying coefficient spatial autoregressive panel model on 2004–2019 panel data, this study shows the following: (i) The relationship between economic growth and carbon emissions forms an “S”-shaped curve, with the contribution decreasing as tertiary industry grows, defining three stages of carbon dependency. (ii) There is significant heterogeneity in carbon dependency across provinces, with some advancing to “weak dependency” or an “economic carbon peak” due to advantages and policies. (iii) Dependency levels shift over time, with “weak dependency” being the predominant stage, though transitions occur. (iv) A positive spatial spillover effect in emissions was noted. This study recommends tailored policies for each provincial-level administrative unit based on their carbon dependency and development stage.

In this paper, we introduce a new class of heterogeneous spatial autoregressive models (heterogeneous SAR models) where the variance parameters are modeled in terms of covariates. In order to estimate the model parameters, as well as their corresponding standard error estimates, we proposed a computational efficient MCMC method which combines the Gibbs sampler with Metropolis-Hastings algorithm. The proposed estimate method is illustrated through numerous simulations and is applied to the Boston housing data.

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.

This paper aims to propose a profile quasi-maximum likelihood estimation method for semiparametric varying-coefficient spatial autoregressive(SVCSAR) panel models with fixed effects. The proposed estimation approach can directly estimate the desired parameters on the basis of B-spline approximations of nonparametric components, and skip the estimation of individual effects. Under some mild assumptions, the consistency for the parametric part and the nonparametric part are given respectively and the asymptotic normality for the parametric part is established. The finite sample performance of the proposed method is investigated through Monte Carlo simulation studies. Finally, a real data analysis of the carbon emission dataset is carried out to illustrate the usefulness of the proposed estimation method.

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

This study introduces a partial functional linear spatial autoregressive model which can explore the relationship between a scalar spatially dependent response variable and predictive variables containing both multiple scalar covariates and a functional covariate. With approximating to the functional coefficient by Karhunen–Loève representation, we propose a Bayesian adaptive Lasso method to simultaneously estimate unknown parameters and select important covariates in the model, which can be performed by combining the Gibbs sampler and the Metropolis–Hastings algorithm. Some simulation studies are conducted and the results show that the proposed Bayesian method behaves well.

Heteroscedasticity is often encountered in spatial-data analysis, so a new class of heterogeneous spatial autoregressive models is introduced in this paper, where the variance parameters are allowed to depend on some explanatory variables. Here, we are interested in the problem of parameter estimation and the variable selection for both the mean and variance models. Then, a unified procedure via double-penalized quasi-maximum likelihood is proposed, to simultaneously select important variables. Under certain regular conditions, the consistency and oracle property of the resulting estimators are established. Finally, both simulation studies and a real data analysis of the Boston housing data are carried to illustrate the developed methodology.

经典的函数型回归模型一般假设模型误差具有等方差性,而在经济学、社会科学等领域会经常遇到数据具有异方差的情形.因此,针对异方差函数型数据,基于方差建模的思想提出了双重部分函数型回归模型,其中方差参数也用函数型协变量进行建模.另外,运用Karhunen-Loève表示定理来逼近函数型系数的思想,以及应用Gibbs抽样和Metropolis-Hastings算法相结合的混合MCMC算法来同时获得均值模型和方差模型中未知参数和函数型系数的贝叶斯估计.最后,通过模拟研究和实际数据分析表明所提出的贝叶斯估计方法是可行有效的.

Functional data widely exists in various fields of society, and functional data analysis has become a hot statistical research direction. Classical functional regression models generally assume that the response variable is an independent variable, but in the fields of economics, environmental science and so on, we often encounter that the response variable has spatial dependence.Therefore, based on functional principal component analysis and MCMC algorithm, Bayesian estimation of the partial functional spatial autoregressive model with the spatial response variable is studied.The idea of approximating functional coefficients by the Karhunen-Lo`eve representation theorem, and the hybrid MCMC algorithm combining Gibbs sampling and Metropolis-Hastings algorithm are used to obtain Bayesian estimation of unknown parameters and functional coefficients in the model. Finally,some simulation studies and empirical analysis of Canadian temperature data show that the proposed Bayesian estimation method is feasible and effective.

We propose a fully Bayesian estimation approach for partially linear varying coefficient spatial autoregressive models on the basis of B-spline approximations of nonparametric components. A computational efficient MCMC method that combines the Gibbs sampler with Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard error estimates. Monte Carlo simulations are used to investigate the finite sample performance of the proposed method. Finally, a real data analysis of Boston housing data is used to illustrate the usefulness of the proposed methodology.

基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.

本文研究泊松逆高斯回归模型的贝叶斯统计推断.基于应用Gibbs抽样,Metropolis-Hastings算法以及Multiple-Try Metropolis算法等MCMC统计方法计算模型未知参数和潜变量的联合贝叶斯估计,并引入两个拟合优度统计量来评价提出的泊松逆高斯回归模型的合理性.若干模拟研究与一个实证分析说明方法的可行性.

Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example.

对响应变量带有不可忽略缺失数据的联合均值与方差模型的贝叶斯估计问题进行了研究.缺失数据机制通过logistic回归模型来指定,模型参数和缺失数据机制参数的联合贝叶斯估计通过运用MH算法及Gibbs抽样获得,并用数值计算阐明上述方法的可行性.

This paper presents the nonparametric quantile regression estimation for the regression function operator when the functional data with the responses missing at random are considered. Then, the large sample properties of the proposed estimator are established under some mild conditions. Finally, a simulation study is conducted to investigate the finite sample properties of the proposed method.