Deep learning for higher-order nonparametric spatial autoregressive model

Deep learning technology has been successfully applied in more and more fields. In this paper, the application of deep neural networks in higher-order nonparametric spatial autoregressive models is studied. For spatial model, we propose the higher-order nonparametric spatial autoregressive neural network (HNSARNN) to fit the model. This method offers both good interpretability and prediction performance, and solves the black box problem in deep learning models to some degree. In various scenarios of spatial data distribution, the proposed method demonstrates superior performance compared to traditional approaches for handling nonparametric functions (such as the B-spline method). Simulation results show the effectiveness of the proposed model.