基于高维精度矩阵的统计推断  

Statistical Inference Based on High-dimensional Precision Matrix

作　　者：王月 刘兵兵[1,2] Wang Yue;Liu Bingbing(School of Management,University of Science and Technology of China,Hefei 230000,China;School of Mathematics and Computational Science,Anqing Normal University,Anqing Anhui 246133,China)

机构地区：[1]中国科学技术大学管理学院,合肥230000 [2]安庆师范大学数学与计算科学学院,安徽安庆246133

出　　处：《统计与决策》2020年第24期5-9,共5页Statistics & Decision

基　　金：安徽高校自然科学研究基金重点项目(KJ2017A361);安徽省高校优秀青年人才支持计划(gxyq2017026)。

摘　　要：文章针对高维精度矩阵,提出了一种新的基于纠偏推断的方法。该方法基于Liu W于2016年提出的快速估计精度矩阵的SCIO方法,通过对初始估计量纠偏,引出纠偏估计量DSCIO的渐近正态分布,从而构造精度矩阵单个元素的置信区间。同时,利用Bootstrap-assisted策略将该方法推广到构造一组元素的同时推断。与现有方法相比,该方法在高维情况下计算效率更高且具有很好的准确性和稳健性。模拟结果表明,DSCIO方法在计算速度和准确度方面都具有明显优势。This paper proposes a new method based on deviation rectification for high-dimensional precision matrix.Based on the SCIO method of rapid estimation accuracy matrix proposed by Liu W in 2016,and throughrectifying the initial estimator,thepaper draws forth the asymptotic normal distribution of the rectifying estimator DSCIO,thus constructing the confidence interval of a single element in the precision matrix.Meanwhile,the paper uses Bootstrap-assisted strategy to promote the method to construct simultaneous inference of a group of elements.Compared with the existing methods,the proposed method is more efficient and enjoys better accuracy and robustness in the case of high dimension.Simulation results show that the DSCIO method has obvious advantages in terms of calculation speed and accuracy.

关 键 词：高维精度矩阵 统计推断 同时置信区间 BOOTSTRAP 

分 类 号：O21[理学—概率论与数理统计]