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Title: The influence function of penalized regression estimators
Authors: Oellerer, Viktoria # ×
Croux, Christophe
Alfons, Andreas #
Issue Date: 2014
Publisher: Gordon and Breach
Series Title: Statistics vol:49 issue:4 pages:741-765
Abstract: To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations non standard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function.
ISSN: 0233-1888
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven
× corresponding author
# (joint) last author

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