Title: Variable selection with spatially autoregressive errors: A generalized moments LASSO estimator
Authors: Arnab Bhattacharjee - Heriot-Watt University (United Kingdom) [presenting]
Liqian Cai - Michigan State University (United States)
Roger Calantone - Michigan State University (United States)
Taps Maiti - Michigan State University (United States)
Abstract: A new penalized variable selection and estimation method under a spatial regression model - a generalized moments LASSO estimator - is proposed as a combination of the LASSO with GMM estimation. We consider the spatial error model where the error term is spatially autoregressive across cross-section units. Statistical properties of penalized estimation methods like LASSO have not been studied under spatial regression models where the errors are not IID. We establish parameter consistency and selection sign consistency of the proposed estimator in the low dimensional setting when the parameter dimension $p$ is fixed and smaller than the sample size $n$, as well as the high dimensional setting when $p$ is greater than and growing with $n$. In both cases, we assume sparsity, that is, the number of non-zero components of the parameter are assumed to be small relative to the number of observations. Finite sample performance of the proposed method is examined by simulation studies, and compared with the traditional LASSO for independent data. The methods are illustrated with an application to hedonic house price model for the Aveiro-lhavo urban housing market in Portugal.