Statistical inference of partially linear varying coefficient spatial autoregressive models

This paper proposes a semiparametric partially linear varying coefficient spatial autoregressive model, which is a generalization of standard spatial autoregressive model and partially linear spatial autoregressive model. To estimate the unknown spatial lag parameter, constant coefficients and coefficient functions, a profile quasi-maximum likelihood approach based on the local-linear method is introduced. To test the existence of the spatial effects, a generalized likelihood ratio test statistic is proposed, and a residual-based bootstrap procedure is used to derive the p-value of the test. Some simulations are conducted to examine the performance of our proposed procedures and the results are satisfactory. Furthermore, a real-world example is given to demonstrate the application of the proposed procedures.