Robust and efficient estimation in ordinal response models using the density power divergence

Abstract

 In real life, we frequently encounter ordinal variables depending upon independent covariates. The latent linear regression model is useful for modelling such data. One can find the model's parameters' maximum likelihood estimate (MLE). Though noted for its optimum properties, a small proportion of outliers may destabilize the MLE. This paper uses the minimum density power divergence estimate (MDPDE) as a robust alternative. The roles of different link functions are analysed in this context. We discuss their asymptotic properties in this setup. Unlike the MLE, the MDPDEs are robust for– lower values of the gross error sensitivity, and very high breakdown point. Also, the slope’s MDPDEs never implode. In simulation studies for pure data, MDPDEs perform almost as good as the MLE. However, the MDPDEs outperform the MLE in data contamination. Moreover, MDPDEs are very competitive with the other robust alternatives. Finally, this article is wrapped up with a real-data example. 

Keywords:

• Latent linear regression model
• Robustness
• Minimum Density Power Divergence Estimator

2020 Mathematics Subject Classification:

• 62F35

Acknowledgments

The authors gratefully acknowledge the comments of the referees and the editorial board which helped to significantly improve this manuscript.

Data availability statement

The data set that supports the findings of this study is openly available in the UCI Machine Learning Repository at https://archive.ics.uci.edu/ml/datasets/wine+quality. See [27] to know more about this data set.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research of AG is partially supported by the INSPIRE Faculty Research Grant from the Department of Science and Technology, Govt. of India, and an internal research grant from the Indian Statistical Institute, India. The research of AB is supported by the Technology Innovation Hub at the Indian Statistical Institute, Kolkata under Grant NMICPS/006/MD/2020-21 of the Department of Science and Technology, Government of India, dated 16.10.2020.