Scalable confidence intervals of precision matrices in high dimensions

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.