Uncertain logistic and Box-Cox regression analysis with maximum likelihood estimation

Abstract

Although the maximum likelihood estimation (MLE) for the uncertain discrete models has long been an academic interest, it has yet to be proposed in the literature. Thus, this study proposes the uncertain MLE for discrete models in the framework of the uncertainty theory, such as the uncertain logistic regression model. We also generalize the estimation proposed by Lio and Liu and obtain the uncertain MLE for non-linear continuous models, such as the uncertain Box-Cox regression model. Our proposed methods provide a useful tool for making inferences regarding non-linear data that is precisely or imprecisely observed, especially data based on degrees of belief, such as an expert’s experimental data. We demonstrate our methodology by calculating proposed estimates and providing forecast values and confidence intervals for numerical examples. Moreover, we evaluate our proposed models via residual analysis and the cross-validation method. The study enriches the definition of the uncertain MLE, thus making it easy to construct estimation and prediction methods for general uncertainty models.

Keywords:

• Maximum likelihood estimation
• uncertain logistic model
• uncertain Box-Cox regression model
• prediction confidence interval
• cross-validation

Acknowledgments

Our deepest gratitude goes to the editors and the journal reviewers for their insightful comments and suggestions that substantially improved this paper.

Additional information

Funding

This work was supported in part by the Beijing Forestry University Education and Teaching Research Project under Grant [2020KCSZ062, BJFU2020JY023] and the Fundamental Research Funds for the Central Universities under Grant [BLX2019446].