A new robust approach for the polytomous logistic regression model based on R\'enyi's pseudodistances

Abstract

This paper presents a robust alternative to the Maximum Likelihood Estimator (MLE) for the Polytomous Logistic Regression Model (PLRM), known as the family of minimum R\`enyi Pseudodistance (RP) estimators. The proposed minimum RP estimators are parametrized by a tuning parameter $\alpha\geq0$, and include the MLE as a special case when $\alpha=0$. These estimators, along with a family of RP-based Wald-type tests, are shown to exhibit superior performance in the presence of misclassification errors. The paper includes an extensive simulation study and a real data example to illustrate the robustness of these proposed statistics.