On the restricted almost unbiased Liu estimator in the logistic regression model

ABSTRACT

It is known that when the multicollinearity exists in the logistic regression model, variance of maximum likelihood estimator is unstable. As a remedy, in the context of biased shrinkage Liu estimation, Chang introduced an almost unbiased Liu estimator in the logistic regression model. Making use of his approach, when some prior knowledge in the form of linear restrictions are also available, we introduce a restricted almost unbiased Liu estimator in the logistic regression model. Statistical properties of this newly defined estimator are derived and some comparison results are also provided in the form of theorems. A Monte Carlo simulation study along with a real data example are given to investigate the performance of this estimator.

KEYWORDS:

• Almost unbiased Liu estimator
• eigenvalue
• Liu estimator
• mean squared error matrix
• restricted almost unbiased Liu estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62J02
• Secondary 62J07

Acknowledgments

The authors are highly obliged to the editor and the reviewers for the comments and suggestions which improved the paper in its present form.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11501072].