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

## Author(s): Zhao, Tuo; Roeder, Kathryn; Liu, Han

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 Abstract: Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. 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. We also report thorough experimental results on text, stock, and genomic datasets. Publication Date: 2014 Electronic Publication Date: 20-Oct-2014 Citation: Zhao, Tuo, Kathryn Roeder, and Han Liu. "Positive semidefinite rank-based correlation matrix estimation with application to semiparametric graph estimation." Journal of Computational and Graphical Statistics 23, no. 4 (2014): 895-922. DOI: doi:10.1080/10618600.2013.858633 ISSN: 1061-8600 EISSN: 1537-2715 Pages: 895 - 922 Type of Material: Journal Article Journal/Proceeding Title: Journal of Computational and Graphical Statistics Version: Author's manuscript