Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data
This addresses the problem of statistical inference in high-dimensional settings with missing data for researchers in fields like biomedicine, though it is incremental as it builds on existing methods with specific improvements.
The paper tackles high-dimensional linear regression with blockwise missing data by proposing a computationally efficient estimator and a debiased estimator for individual coefficients, achieving asymptotically normal distributions and better performance in numerical studies and an Alzheimer's disease application compared to existing methods.
Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.