A Decorrelating and Debiasing Approach to Simultaneous Inference for High-Dimensional Confounded Models

Understand

Motivated by the simultaneous association analysis with the presence of latent confounders, this paper studies the large-scale hypothesis testing problem for the high-dimensional confounded linear models with both non-asymptotic and asymptotic false discovery control.

• Such model covers a wide range of practical settings where both the response and the predictors may be confounded.
• In the presence of the high-dimensional predictors and the unobservable confounders, the simultaneous inference with provable guarantees becomes highly challenging, and the unknown strong dependence among the confounded covariates makes the challenge even more pronounced.
• This paper first introduces a decorrelating procedure that shrinks the confounding effect and weakens the correlations among the predictors, then performs debiasing under the decorrelated design based on some biased initial estimator.