Variable selection for high‐dimensional generalized linear model with block‐missing data
提出一种基于回归的插补算法处理多块缺失数据，先估计稀疏精度矩阵再插补缺失块，理论证明变量选择和估计的一致性，模拟和阿尔茨海默病数据验证其稳健性和优越性。
Abstract In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block‐wise missing data either focus on the single‐block missing pattern or heavily rely on the model structure. In this study, we propose a single regression‐based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block‐wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.