Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem.

In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures.