# New robust statistical procedures for polytomous logistic regression models

## TL;DR

This paper introduces a new family of robust estimators and test statistics for polytomous logistic regression, improving robustness over traditional likelihood-based methods, supported by theoretical analysis, simulations, and real data examples.

## Contribution

It develops minimum density power divergence estimators and Wald-type tests for polytomous logistic regression, offering enhanced robustness over maximum likelihood approaches.

## Key findings

- Robust estimators exhibit lower influence from outliers.
- Simulation studies confirm improved robustness and accuracy.
- Data-driven method effectively selects tuning parameters.

## Abstract

This paper 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 paper 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.