High-dimensional semiparametric bigraphical models

• 成果类型: Article
• 署名作者: Ning, Yang; Liu, Han
• 署名单位: University of Waterloo; Princeton University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast009
• 发表日期: 2013
• 页码: 655670
• 关键词: likelihood ratio test; covariance; product; minimization; separability

摘要

In multivariate analysis, a Gaussian bigraphical model is commonly used for modelling matrix-valued data. In this paper, we propose a semiparametric extension of the Gaussian bigraphical model, called the nonparanormal bigraphical model. A projected nonparametric rank-based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework. Theoretically, our semiparametric procedure achieves the parametric rates of convergence for both matrix estimation and graph recovery. Empirically, our approach outperforms the parametric Gaussian model for non-Gaussian data and is competitive with its parametric counterpart for Gaussian data. Extensions to the categorical bigraphical model and the missing data problem are discussed.