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

Abstract

This paper presents a robust alternative to the maximum likelihood estimator (MLE) for the polytomous logistic regression model, known as the family of minimum Rènyi Pseudodistance (RP) estimators. The proposed minimum RP estimators are parametrized by a tuning parameter $\alpha \ge 0$, 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.