High-dimensional statistical inference via DATE

For high-dimensional statistical inference, de-sparsifying methods have received popularity thanks to their appealing asymptotic properties. Existing results show that aforementioned methods share the same order of o(1) for the secondary bias term in probability. In this paper, we propose the de-sparsifying hard thresholded estimator (DATE) to further reduce the order. More specifically, we demonstrate that the suggested method achieves a smaller order of o( log (n) log (p)) for the secondary bias term with n indicating the sample size and p indicating the dimensionality, yielding generally better performances under finite samples. Furthermore, the proposed method is shown to achieve a tradeoff between the type I error and the average power, suggesting appealing guaranteed reliability. The numerical results confirm that our method yields higher statistical accuracy than other de-sparsifying methods.