High-dimensional robust precision matrix estimation: Cellwise corruption under ϵ\epsilon ϵ-contamination (original) (raw)
2018 High-dimensional robust precision matrix estimation: Cellwise corruption under epsilon\epsilon epsilon-contamination
Po-Ling Loh,Xin Lu Tan
Electron. J. Statist. 12(1): 1429-1467 (2018). DOI: 10.1214/18-EJS1427
Abstract
We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately chosen robust covariance matrix estimators into the graphical Lasso and CLIME. Such estimators were recently proposed in the robust statistics literature, but only analyzed mathematically from the point of view of the breakdown point. This paper provides complementary high-dimensional error bounds for the precision matrix estimators that reveal the interplay between the dimensionality of the problem and the degree of contamination permitted in the observed distribution. We also show that although the graphical Lasso and CLIME estimators perform equally well from the point of view of statistical consistency, the breakdown property of the graphical Lasso is superior to that of CLIME. We discuss implications of our work for problems involving graphical model estimation when the uncontaminated data follow a multivariate normal distribution, and the goal is to estimate the support of the population-level precision matrix. Our error bounds do not make any assumptions about the the contaminating distribution and allow for a nonvanishing fraction of cellwise contamination.
Citation
Po-Ling Loh. Xin Lu Tan. "High-dimensional robust precision matrix estimation: Cellwise corruption under epsilon\epsilon epsilon-contamination." Electron. J. Statist. 12 (1) 1429 - 1467, 2018. https://doi.org/10.1214/18-EJS1427
Information
Received: 1 October 2016; Published: 2018
First available in Project Euclid: 18 May 2018
Digital Object Identifier: 10.1214/18-EJS1427
Subjects:
Primary: 62F35
Secondary: 62G35
Keywords: cellwise contamination, Kendall’s tau, median absolute deviation, Robust covariance matrix estimation, Spearman’s rho
Vol.12 • No. 1 • 2018
