Open Access
November 2017 Influence functions for penalized M-estimators
Marco Avella-Medina
Bernoulli 23(4B): 3178-3196 (November 2017). DOI: 10.3150/16-BEJ841


We study the local robustness properties of general nondifferentiable penalized M-estimators via the influence function. More precisely, we propose a framework that allows us to define rigorously the influence function as the limiting influence function of a sequence of approximating estimators. We show that it can be used to characterize the robustness properties of a wide range of sparse estimators and we derive its form for general penalized M-estimators including lasso and adaptive lasso type estimators. We prove that our influence function is equivalent to a derivative in the sense of distribution theory.


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Marco Avella-Medina. "Influence functions for penalized M-estimators." Bernoulli 23 (4B) 3178 - 3196, November 2017.


Received: 1 January 2015; Revised: 1 March 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778283
MathSciNet: MR3654803
Digital Object Identifier: 10.3150/16-BEJ841

Keywords: distribution theory , implicit function theorem , Lasso , regularization , robust statistics

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 4B • November 2017
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