High-dimensional statistical inference via DATE

Abstract

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 $o(\sqrt{\frac{\hspace{0.17em}\text{log}\hspace{0.17em}(n)}{\hspace{0.17em}\text{log}\hspace{0.17em}(p)}})$ 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.

Keywords:

• Statistical inference
• de-sparsifying
• hard thresholded estimator
• confidence interval
• hypothesis testing

Acknowledgements

The authors sincerely thank the Editor, Production Editor, and the referees for their helpful comments and suggestions that led to substantial improvement of the paper.

Additional information

Funding

This work was supported by National Natural Science Foundation of China-72071187, 11671374, 71731010, and 71921001, and Fundamental Research Funds for the Central Universities-WK3470000017, WK2040000027, and WK2040160028.