Statistical inference for semiparametric varying -coefficient spatial autoregressive models under restricted conditions

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.