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.

摘要

对于高维统计推断，去稀疏化方法因其吸引人的渐近特性而受到欢迎。现有结果表明，上述方法在概率上对二次偏差项具有相同的o (1) 阶。在本文中，我们提出了去稀疏化硬阈值估计器 (DATE) 以进一步降低阶数。更具体地说，我们证明了建议的方法实现了更小的阶数$o(\sqrt{\frac{\hspace{0.17em}\text{日志}\hspace{0.17em}(n)}{\hspace{0.17em}\text{日志}\hspace{0.17em}(p)}})$对于次要偏差项，n表示样本大小，p表示维度，在有限样本下通常会产生更好的性能。此外，所提出的方法被证明可以在 I 类错误和平均功率之间实现权衡，表明具有吸引力的保证可靠性。数值结果证实，我们的方法比其他去稀疏化方法产生更高的统计精度。