Shrinkage estimation in the zero-inflated Poisson regression model with right-censored data

• Published in: Communications in statistics. Theory and methods Vol. 53; no. 13; pp. 4898 - 4917
• Main Authors: Zandi, Zahra, Bevrani, Hossein, Belaghi, Reza Arabi
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.07.2024; Taylor & Francis Ltd
• Subjects: Censored data (mathematics); Estimators; Monte Carlo simulation; Parameter estimation; Performance evaluation; Poisson density functions; preliminary test estimator; Regression models; right-censored data; shrinkage estimators; Stein-type estimators; Zero-inflated Poisson regression
• ISSN: 0361-0926; 1532-415X; 1532-415X
• DOI: 10.1080/03610926.2023.2196751

In this article, we improve parameter estimation in the zero-inflated Poisson regression model using shrinkage strategies when it is suspected that the regression parameter vector may be restricted to a linear subspace. We consider a situation where the response variable is subject to right-censoring. We develop the asymptotic distributional biases and risks of the shrinkage estimators. We conduct an extensive Monte Carlo simulation for various combinations of the inactive predictors and censoring constants to compare the performance of the proposed estimators in terms of their simulated relative efficiencies. The results demonstrate that the shrinkage estimators outperform the classical estimator in certain parts of the parameter space. When there are many inactive predictors in the model, as well as when the censoring percentage is low, the proposed estimators perform better. The performance of the positive Stein-type estimator is superior to the Stein-type estimator in certain parts of the parameter space. We evaluated the estimators' performance using wildlife fish data.