The Influence Function of Graphical Lasso Estimators

Gaëtan Louvet*, Jakob Raymaekers, Germain Van Bever, Ines Wilms

*Corresponding author for this work

Research output: Working paper / PreprintWorking paper

Abstract

The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical lasso (Glasso) gained popularity as they facilitate interpretability, thereby separating pairs of variables that are conditionally dependent from those that are independent (given all other variables). Glasso lacks, however, robustness to outliers. To overcome this problem, one typically applies a robust plug-in procedure where the Glasso is computed from a robust covariance estimate instead of the sample covariance, thereby providing protection against outliers. In this paper, we study such estimators theoretically, by deriving and comparing their influence function, sensitivity curves and asymptotic variances.
Original languageEnglish
PublisherCornell University - arXiv
Number of pages30
Publication statusPublished - 2022

Publication series

SeriesarXiv.org
Number2209.07374
ISSN2331-8422

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