Variable selection and estimation for high-dimensional partially linear spatial autoregressive models with measurement errors

In this paper, we develop a class of corrected post-model selection estimation method to identify important explanatory variables in parametric component of high-dimensional partially linear spatial autoregressive model with measurement errors. Compared with existing methods, the proposed method adds a new process of re-estimating the selected model parameters after model selection. We show that the post-model selection estimator performs at least as well as the Lasso penalty estimator by establishing some theorems of model selection and estimation properties. Extensive simulation studies not only evaluate the finite sample performance of the proposed method, but also show the superiority of the proposed method over other methods. As an empirical illustration, we apply the proposed model and method to two real data sets.