Estimation and inference of partially linear varying coefficient spatial autoregressive models under constraint and heteroskedasticity

Partially linear varying coefficient spatial autoregressive models are a powerful statistical tool for analyzing data with complex features such as nonlinearity, coexistence of homogenous and heterogenous covariate effects and spatial dependence. In this paper, we consider estimation and inference of such models under constraint and heteroskedasticity. By integrating local linear smoothing method, generalized method of moments and Lagrange multiplier method, we obtain constrained estimators of parameters and coefficient functions and study asymptotic properties of the estimators. Moreover, we construct a Wald statistic to test whether regression coefficients satisfy certain constraint, and show that the test statistic asymptotically follows chi-square distribution under null hypothesis as well as global and local alternative hypotheses. Simulation studies show that incorporating constraint and heteroscedasticity can significantly improve estimation accuracy especially for regression coefficients. A real data example is provided to demonstrate the proposed estimation and testing procedures.