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.

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.

With the advent of the post-epidemic era, a great wave of tourism has been ushered in everywhere. The relationship between tourism and mental health has become a hot topic in society. This paper investigates the enhancement of people’s mental health after tourism through social survey. Using Hangzhou as the sample collection site, this paper conducted a study on the role of tourism in enhancing personal mental health through descriptive analysis, factor analysis and structural equation modeling, and further specifically analyzed the role of mediating variables. The results showed that: (1) The purpose of tourism is to relax and relieve stress, and the effectiveness of tourism is mainly reflected in the alleviation of emotional conditions; (2) Factor Analysis reduced the dimensionality of personal mental health indicators, and finally obtained four factors, among which the comprehensive behavioral ability and physiological manifestation had the best improvement effect after tourism; (3) The structural equation model shows that the enhancing effect of tourism on mental health originates from the factor of inner psychological characteristic, and this factor works through two paths: Inner Psychological Characteristic-Social Adaptability-Physiological Manifestations-Enhancement of Mental Health by Tourism, and Inner Psychological Characteristic-Comprehensive Behavioral Ability-Enhancement of Mental Health by Tourism; (4) Tourism has an enhancing effect on personal mental health, and the enhancing effect is most significant among the middle-aged and young people who are unmarried and do not have children yet. These results have been reasonably analyzed and explained, and relevant suggestions are put forward.

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.

This paper studies the variable selection of high-dimensional spatial autoregressive panel models with fixed effects in which a matrix transformation method is applied to eliminate the fixed effects. Then, a penalized quasi-maximum likelihood is developed for variable selection and parameter estimation in the transformed panel model. Under some regular conditions, the consistency and oracle properties of the proposed estimator are established. Some Monte-Carlo experiments and a real data analysis are conducted to examine the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.

研究带固定效应空间自回归面板模型的拟极大似然估计和检验问题.首先通过矩阵变换消除模型中的固定效应项,给出参数的拟极大似然估计,并且建立参数估计的渐近性质.此外,还基于矩阵变换,针对空间自回归系数λ构造LM检验统计量来检验是否显著不为0,推导出该统计量在零假设下的渐近分布.最后通过模拟研究结果证实参数估计及LM检验的有限样本性质,展示提出的估计和检验方法是可行有效的.

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.

This paper considers the problem of variable selection in high-dimensional longitudi-nal linear regression models with monotone missing patterns. A new variable selection procedure is proposed based on the smooth-threshold inverse probability weighted generalized estimating equation. The proposed procedure avoids the convex optimization problem without using penalty functions. Be-sides, the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimate the nonzero regression coefficients. Under some regularity conditions, the variable selection procedure is proved to have Oracle property. Finally, some simulation studies are conducted to examine the finite sample property of the proposed variable selec-tion procedure.

This article is concerned with estimations for longitudinal partial linear models with covariate that is measured with error. We propose a generalized empirical likelihood method by combining correction attenuation and quadratic inference functions. The method takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix. We define a generalized empirical likelihood-based statistic for the regression coefficients and residual adjusted empirical likelihood for the baseline function. The empirical log-likelihood ratios are proven to be asymptotically chi-squared, and the corresponding confidence regions are then constructed. Compared with methods based on normal approximations, the generalized empirical likelihood does not require consistent estimators for the asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.

In this paper, empirical likelihood inference for longitudinal data within the framework of partial linear regression models are investigated. The proposed procedures take into consideration the correlation within groups without involving direct estimation of nuisance parameters in the correlation matrix. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence intervals. A nonparametric version of Wilk's theorem for the limiting distribution of the empirical likelihood ratio is derived. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. The finite sample behaviour of the proposed method is evaluated with simulation and illustrated with an AIDS clinical trial data set.

We propose a novel variable selection for varying coefficient models with longitudinal data. The theoretical properties of the resulting estimators are established. In addition, simulation studies and a real data set are conducted to evaluate the proposed method.