Asymptotic analysis of the Huberized LASSO estimator

Xiaohui Chen, Z. Jane Wang, Martin J. McKeown

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Huberized LASSO model, a robust version of the popular LASSO, yields robust model selection in sparse linear regression. Though its superior performance was empirically demonstrated for large variance noise, currently no theoretical asymptotic analysis has been derived for the Huberized LASSO estimator. Here we prove that the Huberized LASSO estimator is consistent and asymptotically normal distributed under a proper shrinkage rate. Our derivation shows that, unlike the LASSO estimator, its asymptotic variance is stabilized in the presence of noise with large variance. We also propose the adaptive Huberized LASSO estimator by allowing unequal penalty weights for the regression coefficients, and prove its model selection consistency. Simulations confirm our theoretical results.

Original languageEnglish (US)
Title of host publication2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Proceedings
Pages1898-1901
Number of pages4
DOIs
StatePublished - Nov 8 2010
Externally publishedYes
Event2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Dallas, TX, United States
Duration: Mar 14 2010Mar 19 2010

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010
Country/TerritoryUnited States
CityDallas, TX
Period3/14/103/19/10

Keywords

  • Asymptotic normality
  • Huberized LASSO
  • Model selection consistency
  • Robustness
  • Sparse linear regression

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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