Variable selection for spatial autoregressive models

This paper considers variable selection for spatial autoregressive models based on the minimum prediction error criterion. Firstly, based on an initial consistent estimator, a new loss function is constructed from the perspective of prediction, and then we proposed a novel variable selection method. This method can efficiently select the significant variables via penalizing the loss function proposed. Under mild conditions, the large sample properties of the resulting method are established. The finite sample performances are investigated via the extensive Monte Carlo simulations. Finally, this resulting method is applied to the Boston housing price data, further validating the practicability of the proposed method.