Statistical Inference of Partially Linear Spatial Autoregressive Model Under Constraint Conditions

In many application fields of regression analysis, prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients. In this paper, the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions. By combining series approximation method, twostage least squares method and Lagrange multiplier method, the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties. Furthermore, the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions, and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses. Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples. Furthermore, a real example is provided to illustrate the application of the proposed estimation and testing methods.