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

Abstract

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.

2020 Mathematics Subject Classification:

• 62J07
• 62N01
• 62F10
• 62F12

KEYWORDS:

• Zero-inflated Poisson regression
• right-censored data
• preliminary test estimator
• shrinkage estimators
• Stein-type estimators
• Monte Carlo simulation

Acknowledgment

The authors are thankful to the reviewers and Professor Rolf Larsson, at the Department of Mathematics, Uppsala University for their insightful comments and suggestions, which have resulted in a much improved version of this paper.