Variable selection for high-dimensional generalized linear model with block-missing data

Yifan He, Yang Feng, Xinyuan Song

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1279-1297
Number of pages19
JournalScandinavian Journal of Statistics
Issue number3
StatePublished - Sep 2023


  • Lasso
  • block-wise missingness
  • graph model
  • inverse covariance matrix
  • sparsity

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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