Estimation of partially linear single-index spatial autoregressive model using B-splines

Possible dependence across spatial units is a relevant issue in many areas in practice. In this paper, we consider the partially linear single-index spatial autoregressive model to analyze the dependence of the spatial units and suggest an estimation method. An algorithm procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component and the spatial parameter of the model. The nonparametric function is estimated based on B-spline approximation. The Nelder-Mead iteration algorithm is adopted to calculate the parametric and nonparametric parts simultaneously in the optimization. The asymptotic properties of parameter and function estimates are established. Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimation methodology and calculation procedure. Furthermore, we use the proposed method to analyze air quality data and rural household income data in China.