Penalized regression analysis with individual-specific patterns of missing covariates

High-dimensional but incomplete data are common in many settings. With such data, regularized estimation and variable selection techniques developed for complete data fail to produce reliable results due to the missingness. To address this problem, we propose an iterative penalized least squares estimation (IPLSE) method, which customizes existing penalized regression techniques for data with high missing rates and individual-specific missing patterns. The proposed method simultaneously conducts missing value imputation, parameter estimation, and variable selection. Statistical properties are rigorously established, and a simulation demonstrates its competitive performance under various missing patterns, especially when there is missingness concerning important variables. An analysis of China's provincial economic data further supports the merits of the proposed method.