Han, Fang; Han, Xiaoyan; Liu, Han; Caffo, Brian Sparse median graphs estimation in a high-dimensional semiparametric model. (English) Zbl 1391.62128 Ann. Appl. Stat. 10, No. 3, 1397-1426 (2016). 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. Cited in 3 Documents MSC: 62H99 Multivariate analysis 62H12 Estimation in multivariate analysis 62G35 Nonparametric robustness Keywords:graphical model; median graph; complex aggregated data; semiparametric model; high-dimensional statistics; robust estimation PDFBibTeX XMLCite \textit{F. Han} et al., Ann. Appl. Stat. 10, No. 3, 1397--1426 (2016; Zbl 1391.62128) Full Text: DOI arXiv