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Robust and consistent variable selection in high-dimensional generalized linear models

Author

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  • Marco Avella-Medina
  • Elvezio Ronchetti

Abstract

Summary Generalized linear models are popular for modelling a large variety of data. We consider variable selection through penalized methods by focusing on resistance issues in the presence of outlying data and other deviations from assumptions. We highlight the weaknesses of widely-used penalized M-estimators, propose a robust penalized quasilikelihood estimator, and show that it enjoys oracle properties in high dimensions and is stable in a neighbourhood of the model. We illustrate its finite-sample performance on simulated and real data.

Suggested Citation

  • Marco Avella-Medina & Elvezio Ronchetti, 2018. "Robust and consistent variable selection in high-dimensional generalized linear models," Biometrika, Biometrika Trust, vol. 105(1), pages 31-44.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:31-44.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx070
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    Cited by:

    1. Elvezio Ronchetti, 2021. "The main contributions of robust statistics to statistical science and a new challenge," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 127-135, August.
    2. Ana M. Bianco & Graciela Boente & Gonzalo Chebi, 2022. "Penalized robust estimators in sparse logistic regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 563-594, September.

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