中国科学院大学学报2021，Vol.38Issue(2)：171-180,10.DOI:10.7523/j.issn.2095-6134.2021.02.003
基于高维精度矩阵的置信区间的一致性理论
A unified theory of confidence intervals for high-dimensional precision matrix
摘要
Abstract
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.关键词
精度矩阵/高维/bootstrap-assisted/置信区间/同时推断/纠偏Key words
precision matrix/high dimensionality/bootstrap-assisted/confidence intervals/simultaneous inference/de-biased分类
数理科学引用本文复制引用
王月,李阳,郑泽敏..基于高维精度矩阵的置信区间的一致性理论[J].中国科学院大学学报,2021,38(2):171-180,10.基金项目
Supported by National Natural Science Foundation of China (11601501,11671374,and 71731010),Anhui Provincial Natural Science Foundation (1708085QA02),and Fundamcntal Rescarch Funds for the Central Universities (WK2040160028) （11601501,11671374,and 71731010）
