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New robust statistical procedures for the polytomous logistic regression models

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  • Elena Castilla
  • Abhik Ghosh
  • Nirian Martin
  • Leandro Pardo

Abstract

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald‐type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data‐driven selection of the robustness tuning parameter is proposed with empirical justifications.

Suggested Citation

  • Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "New robust statistical procedures for the polytomous logistic regression models," Biometrics, The International Biometric Society, vol. 74(4), pages 1282-1291, December.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:4:p:1282-1291
    DOI: 10.1111/biom.12890
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    Cited by:

    1. Miron, Julien & Poilane, Benjamin & Cantoni, Eva, 2022. "Robust polytomous logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    2. Castilla, Elena & Zografos, Konstantinos, 2022. "On distance-type Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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