Penalized profile quasi-maximum likelihood method of partially linear spatial autoregressive model

In this paper, we develop a class of penalized likelihood method to identify important explanatory variables in parametric component of partially linear spatial autoregressive model. Compared to existing estimation methods, the proposed method can simultaneously select the significant explanatory variables and estimate the nonzero parameters in the parametric component of partially linear spatial autoregressive model. Under appropriate conditions, we establish the consistency, sparsity and asymptotic normality properties of the resulting penalized likelihood estimator. Especially, with proper choice of the penalty function and the regularization parameter, the estimator of the nonzero parameter vector is shown to enjoy the oracle property, in the sense that it is asymptotically normal with the same mean vector and covariance matrix as those it would have if the zero parameters were known in advance. Furthermore, we propose a computationally feasible algorithm to obtain the penalized likelihood estimator. The finite sample performance of the proposed variable selection method is evaluated through extensive simulation studies and illustrated with a real data set.