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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. [ABSTRACT FROM AUTHOR]

This article considers statistical inference for restricted semiparametric varying-coefficient spatial autoregressive(SVCSAR) models. We propose a restricted estimation method for parametric and nonparametric components, and a Lagrange-multiplier-type test for testing hypotheses on the parametric component restrictions of SVCSAR models. Under mild conditions, we obtain the asymptotic normality for the resulting estimator of the parametric vector and the optimal convergence rate for that of nonparametric functions. Simulation studies are carried out to investigate the finite sample performance of the proposed method. The method is exemplified with Boston housing price data. [ABSTRACT FROM AUTHOR]