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Robust groupwise least angle regression

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  • Alfons, Andreas
  • Croux, Christophe
  • Gelper, Sarah

Abstract

Many regression problems exhibit a natural grouping among predictor variables. Examples are groups of dummy variables representing categorical variables, or present and lagged values of time series data. Since model selection in such cases typically aims for selecting groups of variables rather than individual covariates, an extension of the popular least angle regression (LARS) procedure to groupwise variable selection is considered. Data sets occurring in applied statistics frequently contain outliers that do not follow the model or the majority of the data. Therefore a modification of the groupwise LARS algorithm is introduced that reduces the influence of outlying data points. Simulation studies and a real data example demonstrate the excellent performance of groupwise LARS and, when outliers are present, its robustification.

Suggested Citation

  • Alfons, Andreas & Croux, Christophe & Gelper, Sarah, 2016. "Robust groupwise least angle regression," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 421-435.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:421-435
    DOI: 10.1016/j.csda.2015.02.007
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    References listed on IDEAS

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    Cited by:

    1. Zhaoxia Xu & Xiaoping Zhou & Qihu Qian, 2021. "The global sensitivity analysis of slope stability based on the least angle regression," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 105(3), pages 2361-2379, February.
    2. Dries Cornilly & Lise Tubex & Stefan Van Aelst & Tim Verdonck, 2024. "Robust and sparse logistic regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(3), pages 663-679, September.
    3. Smucler, Ezequiel & Yohai, Victor J., 2017. "Robust and sparse estimators for linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 116-130.

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