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

arXiv: https://arxiv.org/abs/2106.03344 · HTML: https://mlsanity.com/paper/2106.03344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 11 of 11)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Structured Matrix Completion with Applications to Genomic Data Integration](https://mlsanity.com/paper/1504.01823/) (2015)
- [Integrating multi-source block-wise missing data in model selection](https://mlsanity.com/paper/1901.03797/) (2019)
- [Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models](https://mlsanity.com/paper/1805.06970/) (2018)
- [Imputation for High-Dimensional Linear Regression](https://mlsanity.com/paper/2001.09180/) (2020)
- [False Discovery Rate Control via Debiased Lasso](https://mlsanity.com/paper/1803.04464/) (2018)
- [A Unified Theory of Confidence Regions and Testing for High Dimensional Estimating Equations](https://mlsanity.com/paper/1510.08986/) (2015)
- [On the prediction loss of the lasso in the partially labeled setting](https://mlsanity.com/paper/1606.06179/) (2016)
- [Generalized Meta-Analysis for Multiple Regression Models Across Studies with Disparate Covariate Information](https://mlsanity.com/paper/1708.03818/) (2017)

## Abstract (arXiv)

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.