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High-dimensional precision matrix estimation: Cellwise corruption under epsilon-contamination

Banff International Research Station for Mathematical Innovation and Discovery

We analyze the statistical consistency of robust estimators for precision matrices in high dimen- sions. Such estimators, formed by plugging robust covariance matrix estimators into the graphical Lasso or CLIME optimization programs, were recently proposed in the robust statistics literature, but only an- alyzed from the point of view of breakdown behavior. As a complementary result, we provide bounds on the statistical error incurred by the precision matrix estimators based on cellwise epsilon-contamination, thus revealing the interplay between the problem dimensions and the degree of contamination permitted in the observed distribution. We discuss implications of our work for problems involving graphical model estimation when the uncontaminated data follow a multivariate normal distribution.

Mathematics; Statistics

video/mp4

Author affiliation: University of Pennsylvania

2016-05-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58172

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/