🤖 AI Summary
This study addresses the sensitivity of conventional maximum likelihood estimation to outliers in modeling proportion data with boundary values, which often leads to biased inference. To overcome this limitation, the authors propose a robust inflated Beta regression estimator that exhibits strong robustness and favorable asymptotic properties. A Wald-type robust test is developed alongside the estimator, and a data-driven adaptive tuning algorithm is introduced to enhance performance. The proposed approach significantly improves robustness while preserving model simplicity and interpretability. Extensive simulations and empirical analyses demonstrate that the method substantially outperforms traditional maximum likelihood estimation in the presence of outliers, offering both theoretical rigor and practical utility.
📝 Abstract
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort inference and lead to misleading conclusions. We propose robust estimators that mitigate the lack of robustness in maximum likelihood-based inference while preserving the simplicity and interpretability of the inflated beta framework. Additionally, an algorithm is introduced to select tuning constants based on the data's robustness requirements. The proposed estimators' asymptotic and robustness properties are studied, and robust Wald-type tests are developed. Simulation studies and a real data application highlight the advantages and practical effectiveness of the proposed robust estimators.