Liu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications

2016/04/08 by Yasin Asar, Asar, Yasin · 1 citation
Chemistry · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Primary 62J07 #Secondary 62J02 #Spectroscopy and Chemometric Analyses

paper · pdf · doi:10.48550/arxiv.1604.02335

openalex publication_date 2016/04/08 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is inflated when there is multicollinearity between the explanatory variables, a new biased estimator is proposed to solve the problem and decrease the variance of MLE in order to make stable inferences. Moreover, we obtain some theoretical comparisons between the new estimator and some others via matrix mean squared error (MMSE) criterion. Furthermore, a Monte Carlo simulation study is designed to evaluate performances of the estimators in the sense of mean squared error. Finally, a real data application is used to illustrate the benefits of new estimator.

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• Almost Unbiased Liu Type Estimator in Bell Regression Model: Theory, Simulation and Application

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