A Note on Small Sample Properties of Estimators in a First-Order Spatial Autoregressive Model

1982 ◽  
Vol 14 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
L Anselin
Keyword(s):  
Monte Carlo Simulation ◽  
Autoregressive Model ◽  
Ad Hoc ◽  
Simulation Experiment ◽  
Small Sample ◽  
Bayesian Estimator ◽  
Spatial Autoregressive Model ◽  
First Order ◽  
Small Sample Properties ◽  
Spatial Autoregressive

This note considers a Bayesian estimator and an ad hoc procedure for the parameters of a first-order spatial autoregressive model. The approaches are derived, and their small sample properties compared by means of a Monte Carlo simulation experiment.

scholarly journals Information Theory Estimators for the First-Order Spatial Autoregressive Model

Entropy ◽  
2012 ◽  
Vol 14 (7) ◽  
pp. 1165-1185 ◽  
Author(s):  
Evgeniy V. Perevodchikov ◽  
Thomas L. Marsh ◽  
Ron C. Mittelhammer
Keyword(s):  
Information Theory ◽  
Autoregressive Model ◽  
Spatial Autoregressive Model ◽  
First Order ◽  
Spatial Autoregressive

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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