Correlation adjusted debiased Lasso: debiasing the Lasso with inaccurate covariate model.

The article addresses the challenge of estimating a low-dimensional parameter β in high-dimensional linear regression models when the nuisance parameter and covariate distribution are unknown or only inaccurately estimated. It introduces the correlation adjusted debiased Lasso (CAD) estimator, which corrects biases present in naive and standard debiasing methods by incorporating degrees-of-freedom and correlation adjustments that account for the dependence and overlap in estimating nuisance parameters. Theoretical results establish that CAD achieves consistent and nearly unbiased estimation of β under proportional asymptotics, even when the precision model is dense or estimated from limited data, a setting where previous methods fail. Extensive simulations demonstrate CAD’s superior bias correction and approximate normality compared to existing estimators, and the work also provides a general joint characterization of simultaneous regression estimators that underpins these findings.