Title: Debiasing the Debiased Lasso with Bootstrap,
Abstract: 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.