A new robust approach for the polytomous logistic regression model based on Rényi's pseudodistances

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Maximum Likelihood Estimator (MLE) is standard for polytomous logistic regression.
• MLE can be sensitive to data misclassification errors.
• Robust alternatives are needed for real-world data.

Purpose of the Study:

• Introduce a new family of robust estimators for polytomous logistic regression.
• Evaluate the performance of these estimators in the presence of misclassification.
• Provide a robust alternative to MLE for improved statistical modeling.

Main Methods:

• Developed minimum Rènyi Pseudodistance (RP) estimators parametrized by a tuning parameter alpha (α).
• Included MLE as a special case (α=0).
• Proposed RP-based Wald-type tests and conducted extensive simulations and a real data analysis.

Main Results:

• Minimum RP estimators demonstrated superior performance compared to MLE under misclassification.
• The proposed RP-based Wald-type tests were also robust to misclassification errors.
• Simulation studies and real data analysis confirmed the robustness and effectiveness of the proposed methods.

Conclusions:

• The family of minimum RP estimators provides a robust alternative to MLE for polytomous logistic regression.
• These estimators are particularly advantageous when dealing with data prone to misclassification.
• The proposed methods enhance the reliability of statistical inference in challenging data scenarios.