Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression

Understand

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random covariates.

• Building upon a high-dimensional EM algorithm, we propose an iterative procedure for estimating the two regression vectors and establish their rates of convergence.
• Based on the iterative estimators, we further construct debiased estimators and establish their asymptotic normality.
• For individual coordinates, confidence intervals centered at the debiased estimators are constructed.