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

Tuo Zhao, Kathryn Roeder, Han Liu

Research output: Contribution to journalArticle

12 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)895-922
Number of pages28
JournalJournal of Computational and Graphical Statistics
Volume23
Issue number4
DOIs
StatePublished - Oct 25 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

Keywords

  • Graphical model
  • High-dimensional statistics
  • Model selection/Variable selection
  • Multivariate analysis
  • Numerical optimization

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