Robust Tail Index Estimation under Random Censoring via Minimum Density Power Divergence

We introduce a robust estimator for the tail index of a Pareto-type distribution under random right censoring, developed within the framework of the minimum density power divergence. To the best of our knowledge, this is the first approach to integrate density power divergence into the context of randomly censored extreme value models, thus opening a new path for robust inference in this setting. Under general regularity conditions, the proposed estimator is shown to be consistent and asymptotically normal. Its finite-sample behavior is thoroughly assessed through an extensive simulation study, which highlights its improved robustness and efficiency compared to existing methods. Finally, the practical relevance of the method is illustrated through an application to a real AIDS survival dataset.