Debiasing the Debiased Lasso with Bootstrap
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In this paper, we prove that under proper conditions, bootstrap can further debias the debiased Lasso estimator for statistical inference of low-dimensional parameters in high-dimensional linear regression. We prove that the required sample size for inference with bootstrapped debiased Lasso, which involves the number of small coefficients, can be of smaller order than the existing ones for the debiased Lasso. Therefore, our results reveal the benefits of having strong signals. Our theory is supported by results of simulation experiments, which compare coverage probabilities and lengths of confidence intervals with and without bootstrap, with and without debiasing.
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