Estimation of partially linear single-index spatial autoregressive model

2019 ◽  
Author(s):  
Suli Cheng ◽  
Jianbao Chen
Keyword(s):  
Autoregressive Model ◽  
Spatial Autoregressive Model ◽  
Single Index ◽  
Partially Linear ◽  
Spatial Autoregressive

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.

scholarly journals Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1448
Author(s):  
Xuan Liu ◽  
Jianbao Chen
Keyword(s):  
Variable Selection ◽  
Autoregressive Model ◽  
Rapid Development ◽  
Heterogeneous Data ◽  
Spatial Effect ◽  
Spatial Effects ◽  
Spatial Autoregressive Model ◽  
Monte Carlo Studies ◽  
Spatial Autoregressive ◽  
Theoretical Results

Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses on variable selection in the spatial autoregressive model with autoregressive disturbances (SARAR) which contains a more comprehensive spatial effect. The variable selection procedure is presented by using the so-called penalized quasi-likelihood approach. Under suitable regular conditions, we obtain the rate of convergence and the asymptotic normality of the estimators. The theoretical results ensure that the proposed method can effectively identify spatial effects of dependent variables, find spatial heterogeneity in error terms, reduce the dimension, and estimate unknown parameters simultaneously. Based on step-by-step transformation, a feasible iterative algorithm is developed to realize spatial effect identification, variable selection, and parameter estimation. In the setting of finite samples, Monte Carlo studies and real data analysis demonstrate that the proposed penalized method performs well and is consistent with the theoretical results.

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