There are great challenges to the analysis of spatially dependent data with the heterogeneity,the endogeneity of spatial weights,and the high-dimensional characteristics of explanatory variables.Based on the robust estimation advantage of Expectile regression and the effective dimensionality reduction ability of penalty compression,we give the two-step and three-step penalty Expectile estimation of unknown parameters of high-dimensional spatial lag models under the exogenous and endogenous spatial weight matrices respectively,and prove the consistency of the proposed estimation and the Oracle property of variable selection under conventional regularization conditions.The numerical simulation demonstrates that the two-step estimation method can work well with the robust statistical problem under the exogenous spatial weight matrix,and the three-step estimation method has excellent performance under the exogenous and endogenous spatial weights.Finally,the effectiveness of the proposed method is further verified by analyzing the relationship between the urban air quality and the economic development in China.
关键词
空间滞后模型/Expectile回归/变量选择/内生性/高维数据
Key words
spatial lag model/Expectile regression/variable selection/endogeneity/high-dimensional data
维普
万方数据