Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, so that some of them have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion. The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.
📌 3 Key Takeaways
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Objective & Hypothesis:Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, so that some of them have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion. The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.
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Key Findings & Data:Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, so that some of them have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion. The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.
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Conclusion & Impact:Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, so that some of them have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion. The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Monte Carlo Simulation · Over-dispersion · Shrinkage Estimators
Abstract
Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, so that some of them have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion. The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.
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