Performance of the shrinkage preliminary test ridge regression estimators based on the conflicting of W, LR and LM tests

Abstract

The shrinkage preliminary test ridge regression estimators (SPTRRE) based on the Wald (W), the likelihood ratio (LR) and the Lagrangian multiplier (LM) tests are considered in this paper. The bias and the risk functions of the proposed estimators are derived. The regions of optimality of the estimators are determined under the quadratic risk function. Under the null hypothesis, the SPTRRE based on LM test has the smallest risk, followed by the estimators based on LR and W tests. However, the SPTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both ridge and departure parameters are discussed. The optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative ridge parameters.

Keywords:

• Dominance
• Lagrangian multiplier
• Likelihood ratio test
• Risk
• Preliminary test
• Ridge regression
• Shrinkage estimation
• Wald test

Acknowledgements

The author is grateful to the referee for his/her comments/suggestions which improved this paper in its present form. He is also thankful to the Dean of the College of Arts and Sciences of Florida International University for awarded him summer 2002 research award.