Variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters

In this article, we consider variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters, in which the explanatory variables include infinite dimensional predictor procedure, treated as functional data, and multiple real valued scalar variate. By combining series approximation method, two-stage least squares method and a class of non convex penalty function, we propose a variable selection method to simultaneously select significant explanatory variables in the parametric component and estimate the corresponding parameter related to spatial lag of the response variable. Under appropriate conditions, we derive the rate of convergence of the series estimator of the functional and parametric component, and show that the proposed variable selection method processes the oracle property. That is, it can estimate the zero components as exact zero with high probability, and estimate the non zero components as efficiently as if the true model was known beforehand. Simulation result show that our proposed variable selection method has better finite sample property.Notably, in the case where the correlation among the explanatory variables in the parametric component is low, the proposed variable selection method performs well. An application of the proposed variable selection method serves as a practical illustration.