Efficient estimation of precision matrices with factor models in high dimension

We present novel contributions to the estimation of sparse precision matrices in high-dimensional settings. First, we introduce Autometrics as a dimension reduction tool that enhances both sparsity and the accuracy of precision matrix estimation. Second, we propose a regression-based Cholesky decomposition approach for estimating the precision matrix. To assess the performance of our methods, we employ factor models and conduct a comprehensive simulation study. The results demonstrate that Autometrics performs on par with, and in some cases outperforms, the Lasso. Furthermore, our regression-based Cholesky decomposition generally surpasses existing approaches, particularly the residual-based feasible nodewise regression. Lastly, we provide an empirical application that confirms the consistency and practical effectiveness of our proposed methods on real-world data.