Moran’s <i>I</i> lasso for models with spatially correlated data

Summary This paper proposes a lasso-based estimator which uses information embedded in the Moran statistic to develop a selection procedure called Moran’s I lasso (Mi-lasso) to solve the eigenvector spatial filtering (ESF) eigenvector selection problem. ESF uses a subset of eigenvectors from a spatial weights matrix to efficiently account for any omitted spatially correlated terms in a classical linear regression framework, thus eliminating the need for the researcher to exlicitly specify the spatially correlated parts of the model. We proposed the first ESF procedure accounting for post-selection inference. We derive performance bounds and show the necessary conditions for consistent eigenvector selection. The key advantages of the proposed estimator are that it is intuitive, theoretically grounded, able to provide robust inference, and substantially faster than lasso based on cross-validation or any proposed forward stepwise procedure. Our simulation results and an application on house prices demonstrate that Mi-lasso performs well compared with existing procedures in finite samples.