Estimation of nonparametric additive models with high order spatial autoregressive errors

In this article, we propose nonparametric generalized method of moments estimation for nonparametric additive models with high order spatial autoregressive dependence. The estimation procedure is derived in three steps by combining a spline-backfitting method with generalized moment conditions that relieve correlations within the dependent variables. Consistency and asymptotic normality are demonstrated under mild conditions. Specifically, compared with estimators of nonparametric functions that ignore cross-sectional dependence in errors, the resultant estimators that consider the error term are asymptotically more efficient and achieve the well-known oracle properties. Simulation studies investigating the finite sample performance of the estimation procedure confirm the validity of our asymptotic theory. An application to the Boston housing data serves as a practical illustration.