Variable selection of partially linear varying coefficient spatial autoregressive model

The partially linear varying coefficient spatial autoregressive model is a recently proposed semi-parametric spatial autoregressive model, in which some of the explanatory variables have varying coefficients while the remained explanatory variables possess constant ones. Although some estimation methods have been proposed for the partially linear varying coefficient spatial autoregressive model, the problem of selecting important explanatory variables in the parametric component of such model has not been addressed to date. In this paper, we propose a penalized profile least squares method to address this problem. Different from the existing estimation methods, the proposed method can simultaneously select the significant explanatory variables in the parametric component and estimate the corresponding nonzero regression coefficients. Furthermore, we provide a computationally feasible algorithm to obtain the penalized profile least squares estimator. The finite sample performance of the proposed variable selection method is evaluated through some simulation studies and illustrated by a real data example.