Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data

Abstract

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.

V2: 40 pages, 2 figures. Accepted at Statistica Sinica

References in corpus (6)

• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• Efficient and Adaptive Linear Regression in Semi-Supervised Settings
• Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models
• Semi-Supervised linear regression
• Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression
• High-dimensional semi-supervised learning: in search for optimal inference of the mean