More on the Bias and Variance Comparisons of the Restricted Almost Unbiased Estimators

Abstract

Sarkar (1992) and Kaç\i ranlar et al. (1999), respectively, proposed the restricted ridge regression estimator (RRE) and restricted Liu estimator (RLE) to combat the well-known multicollinearity problem in linear regression. In this article, the restricted almost unbiased ridge estimator (RAURE) based on the RRE by Sarkar (1992) and the restricted almost unbiased Liu estimator (RAULE) by Kaç\i ranlar et al. (1999) are introduced. The biases and variance matrices of the proposed estimators are derived and compared with the corresponding competitors in literatures. Furthermore, a Monte Carlo evaluation of the estimators is given to illustrate some of the theoretical results.

Keywords:

• Almost unbiased estimator
• Linear restrictions
• Liu estimator
• Multicollinearity
• Ridge regression

2000 Mathematics Subject Classification:

• Primary 62J05
• 62F30

Acknowledgment

The authors are grateful to the anonymous referee for his/her helpful and detail suggestions which led to vast improvement in the presentation of the article. This research was supported by the Fundamental Research Funds for the Central Universities CDJZR10100001.