Positive Semidefinite Rank-based Correlation Matrix Estimation with Application to Semiparametric Graph Estimation.

Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this paper, we illustrate this fundamental tradeoff by studying a semi-parametric 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 paper focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.