Robust precision matrix estimation via weighted median regression with regularization

Abstract

A precision matrix is an important parameter of interests because its elements describe useful association information among multiple variables, which has a wide variety of applications. For example, it is used for inferring gene regulation networks in genomic studies and stock association networks in financial studies. However, in many cases, the precision matrix needs to be robustly estimated due to the presence of outliers. We propose estimating a sparse scaled precision matrix via weighted median regression with regularization. Our weighted median regression approach is consistent under various distributional assumptions including multivariate t- or contaminated Gaussian distributions. This fact is illustrated with simulation studies and a real data analysis with monthly stock return data. The Canadian Journal of Statistics 46: 265-278; 2018 (c) 2018 Statistical Society of Canada