On a new class of binomial ridge-type regression estimators

Abstract

This paper is about developing a new class of two-parameter shrinkage estimators for the binomial model under the multicollinearity problem. The proposed class includes the ridge estimator (RE) and the maximum likelihood estimator (MLE) as special cases. The necessary and sufficient conditions that ensure the superiority of the proposed estimator over the MLE and the RE in terms of the mean squared error (MSE) matrix were obtained. The performance of new estimators is evaluated and compared with the MLE and some REs through simulation under moderate to strong correlations. A real application supports the simulation results.

Keywords:

• Binomial model
• Maximum likelihood
• Multicollinearity
• Ridge estimator
• Shrinkage estimators

Mathematics Subject Classification:

• 62J07

Acknowledgments

The author would like to express his appreciation to the reviewers and the associate editor for their insightful comments, which have helped him to improve his manuscript.

Notes

1 The data set could be downloaded from: http://www1.aucegypt.edu/faculty/hadi/RABE5/Data5/P339.txt.