A two-parameter estimator in the negative binomial regression model

In this article, a two-parameter estimator is proposed to combat multicollinearity in the negative binomial regression model. The proposed two-parameter estimator is a general estimator which includes the maximum likelihood (ML) estimator, the ridge estimator (RE) and the Liu estimator as special ca...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2014-01, Vol.84 (1), p.124-134
Main Authors: Huang, Jiewu, Yang, Hu
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Estimating techniques
Liu estimator
Matrix
maximum likelihood estimator
Maximum likelihood method
mean-squared error
mean-squared error matrix
Monte Carlo simulation
negative binomial regression
Parameter estimation
Regression analysis
ridge estimator
two-parameter estimator
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Summary:In this article, a two-parameter estimator is proposed to combat multicollinearity in the negative binomial regression model. The proposed two-parameter estimator is a general estimator which includes the maximum likelihood (ML) estimator, the ridge estimator (RE) and the Liu estimator as special cases. Some properties on the asymptotic mean-squared error (MSE) are derived and necessary and sufficient conditions for the superiority of the two-parameter estimator over the ML estimator and sufficient conditions for the superiority of the two-parameter estimator over the RE and the Liu estimator in the asymptotic mean-squared error (MSE) matrix sense are obtained. Furthermore, several methods and three rules for choosing appropriate shrinkage parameters are proposed. Finally, a Monte Carlo simulation study is given to illustrate some of the theoretical results.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2012.696648