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Robust adaptive LASSO in high-dimensional logistic regression

Author

Listed:
  • Ayanendranath Basu

    (Indian Statistical Institute)

  • Abhik Ghosh

    (Indian Statistical Institute)

  • Maria Jaenada

    (Statistics and O.R., Complutense University of Madrid)

  • Leandro Pardo

    (Statistics and O.R., Complutense University of Madrid)

Abstract

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood loss function are sensitive to data contamination and other noise and, hence, robust methods are needed for stable and more accurate inference. In this paper, we propose a family of robust estimators for sparse logistic models utilizing the popular density power divergence based loss function and the general adaptively weighted LASSO penalties. We study the local robustness of the proposed estimators through its influence function and also derive its oracle properties and asymptotic distribution. With extensive empirical illustrations, we demonstrate the significantly improved performance of our proposed estimators over the existing ones with particular gain in robustness. Our proposal is finally applied to analyse four different real datasets for cancer classification, obtaining robust and accurate models, that simultaneously performs gene selection and patient classification.

Suggested Citation

  • Ayanendranath Basu & Abhik Ghosh & Maria Jaenada & Leandro Pardo, 2024. "Robust adaptive LASSO in high-dimensional logistic regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(5), pages 1217-1249, November.
    • Handle: RePEc:spr:stmapp:v:33:y:2024:i:5:d:10.1007_s10260-024-00760-2
    DOI: 10.1007/s10260-024-00760-2
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    References listed on IDEAS

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    4. A. Basu & A. Mandal & N. Martin & L. Pardo, 2015. "Robust tests for the equality of two normal means based on the density power divergence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 611-634, July.
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