New Robust Statistical Procedures for the Polytomous Logistic Regression Models

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...

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Bibliographic Details
Published in:Biometrics 2018-12, Vol.74 (4), p.1282-1291
Main Authors: Castilla, Elena, Ghosh, Abhik, Martin, Nirian, Pardo, Leandro
Format: Article
Language:English
Subjects:
BIOMETRIC METHODOLOGY
Computer simulation
Divergence
Economic models
Empirical analysis
Function analysis
Influence function
Influence functions
Maximum likelihood estimators
Minimum density power divergence estimators
Parameter robustness
Polytomous logistic regression
Regression analysis
Regression models
Robustness
Robustness (mathematics)
Statistical analysis
Statistical inference
Statistical tests
Statistics
Wald‐type test statistics
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Summary: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.
ISSN:0006-341X
1541-0420
DOI:10.1111/biom.12890