Moran’s I lasso for models with spatially correlated data
提出一种基于莫兰统计量的套索估计方法（Mi-lasso），用于解决特征向量空间滤波中的特征向量选择问题，具有理论依据、稳健推断且计算速度快于交叉验证套索。
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.