scholarly journals Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1635
Author(s):  
Zhiyong Chen ◽  
Jianbao Chen
Keyword(s):  
Spatial Data ◽  
Generalized Method Of Moments ◽  
Bayesian Estimator ◽  
Posterior Distributions ◽  
Computationally Efficient ◽  
Partially Linear ◽  
Spatial Autoregressive ◽  
Method Of Moments Estimator ◽  
Spatial Autoregressive Models ◽  
Convergent Algorithm

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

scholarly journals PQMLE of a Partially Linear Varying Coefficient Spatial Autoregressive Panel Model with Random Effects

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2057
Author(s):  
Shuangshuang Li ◽  
Jianbao Chen ◽  
Danqing Chen
Keyword(s):  
Random Effects ◽  
Spatial Data ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Finite Sample ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Panel Model ◽  
Spatial Autoregressive ◽  
Quasi Maximum Likelihood

This article deals with asymmetrical spatial data which can be modeled by a partially linear varying coefficient spatial autoregressive panel model (PLVCSARPM) with random effects. We constructed its profile quasi-maximum likelihood estimators (PQMLE). The consistency and asymptotic normality of the estimators were proved under some regular conditions. Monte Carlo simulations implied our estimators have good finite sample performance. Finally, a set of asymmetric real data applications was analyzed for illustrating the performance of the provided method.

scholarly journals Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhiyong Chen ◽  
Minghui Chen ◽  
Guodong Xing
Keyword(s):  
Spatial Data ◽  
Autoregressive Model ◽  
Estimation Method ◽  
Additive Model ◽  
Housing Price ◽  
Nonlinear Effects ◽  
Spatial Autoregressive Model ◽  
Unknown Parameters ◽  
Partially Linear ◽  
Spatial Autoregressive

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.

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