可延展的高维精度矩阵的置信区间

Scalable confidence intervals of precision matrices in high dimensions

针对高维精度矩阵置信区间存在的计算效率低下的问题,提出了De-SCIO统计量.相比较其他方法,基于De-SCIO统计量构造的置信区间计算效率得到了很大的提升,并且它的平均覆盖率更接近于真实覆盖率.De-SCIO统计量构造简单,避免了复杂的理论推导.在合理的条件假设下,证明了De-SCIO统计量的渐近正态性.模拟实验以及实例分析展示了该方法在平均覆盖率和计算效率上的优势.

In order to solve the problem of the computational inefficiency in confidence intervals of high-dimensional precision matrices,the De-SCIO was proposed.Compared with other methods,the computational efficiency of the confidence intervals based on De-SCIO statistic are greatly improved,and their average coverage is closer to the true level.The construction of the De-SCIO statistic is simple and avoids complicated theoretical derivation.Under reasonable assumptions,the asymptotic normality of the De-SCIO statistic was proved.The advantages of this method in average coverage and computational efficiency were demonstrated by the numerical studies and real data example.