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

TL;DR

This paper develops a new statistical inference method for high-dimensional linear regression models with blockwise missing data, enabling accurate estimation and hypothesis testing in complex data integration scenarios.

Contribution

It introduces a computationally efficient estimator using unbiased estimating equations and a novel bias-correction technique for individual coefficients.

Findings

Proposed estimator achieves optimal convergence rates.

Nearly unbiased, asymptotically normal estimators for coefficients.

Method outperforms existing approaches in real data applications.

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.