随着高维数据的不断发展，精度矩阵作为衡量变量间条件相依性的有效工具引起广泛关注。尽管已有大量文献研究精度矩阵，但如何发展一种低计算成本的方法构造高维精度矩阵的同时推断变得尤为迫切。基于nodewise Lasso估计量，利用bootstrap assisted策略构造同时置信区间。与现有方法相比，该方法在理论上不需要不可解释性条件且计算成本非常低。进一步，总结出在次高斯情形下，精度矩阵同时置信区间的一致性理论，即只要精度矩阵某些估计性质满足，该方法可以基于不同的精度矩阵估计方法进行推断。此外，不同于传统的Bonferroni-Holm，该方法是渐近非保守的。模拟结果验证了该方法的优势。
Precision matrix inference is of fundamental importance nowadays in high-dimensional data analysis for measuring conditional dependence. Despite the fast growing literature, developing approaches to make simultaneous inference for precision matrix with low computational cost is still in urgent need. In this paper, we apply bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional precision matrix based on the recent de-biased nodewise Lasso estimator, which does not require the irrepresentability condition and is easy to implement with low computational cost. Furthermore, we summary a unified framework to perform simultaneous confidence intervals for high-dimensional precision matrix under the sub-Gaussian case. We show that as long as some precision matrix estimation effects are satisfied, our procedure can focus on different precision matrix estimation methods which owns great flexibility. Besides, distinct from earlier Bonferroni-Holm procedure, this bootstrap method is asymptotically nonconservative. Both numerical results confirm the theoretical results and computational advantage of our method.
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