Testing a polynomial relationship of the non-parametric component in partially linear spatial autoregressive models

A statistical test procedure is proposed to check a polynomial relationship of the non-parametric component in partially linear spatial autoregressive models, in which a residual-based bootstrap procedure is used to derive the p-value of the test. Some simulations are conducted to assess the performance of the test and the results show that the bootstrap approximation to the null distribution of the test statistic is valid and the test is powerful in identifying a polynomial relationship of the non-parametric component. Furthermore, a real-world example is given to demonstrate the usefulness of the proposed test.