A Variable Selection Method for Spatial Autoregressive Models

• Activity Number: 310
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Liqian Cai* and Tapabrata Maiti and Arnab Bhattacharjee
• Companies: Michigan State University and Michigan State University and Heriot-Watt University
• Keywords: Spatial autoregressive model ; generalized moments estimator ; Lasso ; variable selection ; parameter consistency ; sign consistency

Abstract

Spatial Autoregressive Model is one of the most widely referenced models for cross sectional data which captures the spatial dependence and imposes the structure onto a model. In this paper, we construct a variable selection and estimation method, i.e. a two-stage Lasso-type of estimator for the spatial autoregressive model. We first replace the nuisance parameter with a consistent generalized moments estimator and then apply Lasso to select the number of non-zero components in the parameter of interest. We further develop the estimation consistency and selection sign consistency of the parameter under the low dimensional setting when the dimension of the parameter p is fixed and smaller than the sample size n, as well as the high dimensional setting when p can be larger than, or even growing exponentially with n. The validation of the proposed method is shown by simulation studies.