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Joint estimation of multiple high‐dimensional Gaussian copula graphical models
Author(s) -
He Yong,
Zhang Xinsheng,
Ji Jiadong,
Liu Bin
Publication year - 2017
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12198
Subject(s) - estimator , mathematics , copula (linguistics) , gaussian , graphical model , parametric statistics , algorithm , mathematical optimization , robustness (evolution) , rate of convergence , computer science , statistics , physics , quantum mechanics , econometrics , computer network , biochemistry , chemistry , channel (broadcasting) , gene
Summary A joint estimation approach for multiple high‐dimensional Gaussian copula graphical models is proposed, which achieves estimation robustness by exploiting non‐parametric rank‐based correlation coefficient estimators. Although we focus on continuous data in this paper, the proposed method can be extended to deal with binary or mixed data. Based on a weightedℓ ∞ / ℓ 1minimisation problem, the estimators can be obtained by implementing second‐order cone programming. Theoretical properties of the procedure are investigated. We show that the proposed joint estimation procedure leads to a faster convergence rate than estimating the graphs individually. It is also shown that the proposed procedure achieves an exact graph structure recovery with probability tending to 1 under certain regularity conditions. Besides theoretical analysis, we conduct numerical simulations to compare the estimation performance and graph recovery performance of some state‐of‐the‐art methods including both joint estimation methods and estimation methods for individuals. The proposed method is then applied to a gene expression data set, which illustrates its practical usefulness.