Statistical inference of partially specified spatial autoregressive model

2015 ◽  
Vol 31 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Yuan-qing Zhang ◽  
Guang-ren Yang
Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1448
Author(s):  
Xuan Liu ◽  
Jianbao Chen

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.


2014 ◽  
Vol 2 (3) ◽  
pp. 226-235
Author(s):  
Yuanqing Zhang

Abstract In this paper, we study estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, we propose an instrumental variable estimation. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-n consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and also asymptotically distributed though at a rate slower than root-n. Monte Carlo simulations verify our theory and the results suggest that the proposed method has some practical value.


1982 ◽  
Vol 14 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
L Anselin

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.


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