Estimating the Unrestricted and Restricted Liu Estimators for the Poisson Regression Model: Method and Application

• Published in: Computational economics Vol. 58; no. 2; pp. 311 - 326
• Main Authors: Månsson, Kristofer, Kibria, B. M. Golam
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-08-2021; Springer Nature B.V
• Subjects: Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Eigenvalues; Estimators; Gene expression; Liu estimator; Math Applications in Computer Science; Maximum likelihood; Monte Carlo simulations; MSE; Multicollinearity; Operations Research/Decision Theory; Parameter estimation; Poisson density functions; Poisson regression; Regression models; Restricted estimator; Simulation; Liu estimator; Monte Carlo simulations; Primary 62J07; Multicollinearity; Secondary 62J02; Maximum likelihood; Restricted estimator; MSE; Poisson regression
• ISSN: 0927-7099; 1572-9974; 1572-9974
• DOI: 10.1007/s10614-020-10028-y

This paper considers both unrestricted and restricted Liu estimators in the presence of multicollinearity for the Poisson regression model. It also considers some new estimators of the shrinkage parameter for both unrestricted and restricted Liu estimators. Based on a simulation study and its empirical application, we found that the restricted estimator outperforms the unrestricted one. Further, the restricted Liu estimator also outperforms both the unrestricted Liu and restricted Liu estimators. Hence, this new method is a preferred option when the coefficient vector
β
may belong to a linear sub-space defined by
Rβ 
= 
r
.