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

Marco Avella-Medina and Elvezio Ronchetti

Biometrika, 2018, vol. 105, issue 1, 31-44

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.

Keywords: Contamination neighbourhood; Generalized linear model; Infinitesimal robustness; Lasso; Oracle estimator; Robust quasilikelihood (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asx070 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:105:y:2018:i:1:p:31-44.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().