Sparse median graphs estimation in a high-dimensional semiparametric model. (English) Zbl 1391.62128

Summary: We propose a unified framework for conducting inference on complex aggregated data in high-dimensional settings. We assume the data are a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.


62H99 Multivariate analysis
62H12 Estimation in multivariate analysis
62G35 Nonparametric robustness
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