Model selection and post estimation based on a pretest for logistic regression models

ABSTRACT

This article addresses the problem of parameter estimation of the logistic regression model under subspace information via linear shrinkage, pretest, and shrinkage pretest estimators along with the traditional unrestricted maximum likelihood estimator and restricted estimator. We developed an asymptotic theory for the linear shrinkage and pretest estimators and compared their relative performance using the notion of asymptotic distributional bias and asymptotic quadratic risk. The analytical results demonstrated that the proposed estimation strategies outperformed the classical estimation strategies in a meaningful parameter space. Detailed Monte-Carlo simulation studies were conducted for different combinations and the performance of each estimation method was evaluated in terms of simulated relative efficiency. The results of the simulation study were in strong agreement with the asymptotic analytical findings. Two real-data examples are also given to appraise the performance of the estimators.

KEYWORDS:

• Subspace information
• linear shrinkage estimator
• preliminary test estimator
• asymptotic distributional bias
• asymptotic quadratic risk

AMS SUBJECT CLASSIFICATION:

• 62F10
• 62F12

Acknowledgments

Thanks are due to the editor and referees for their valuable input while reading the manuscript, which resulted in the present form, and part of this research was completed when Professor S. E. Ahmed was visiting Thammasat University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Supranee Lisawadi  http://orcid.org/0000-0002-3214-4610

Muhammad Kashif Ali Shah  http://orcid.org/0000-0003-1741-3701