Some Interesting Properties of the Liu Estimator

• Activity Number: 521
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marvin Haskel Jack Gruber*+
• Companies: Rochester Institute of Technology
• Keywords: ridge type estimator ; shrinkage estimator ; multicollinearity ; biasing parameter

Abstract

In a 1993 paper Liu proposed an estimator that is similar in form but different from the ridge regression estimator of Hoerl and Kennard. More recently in 2007 Ozkale and Kaciranlar proposed a two parameter variation of the Liu estimator. This new estimator has a number of interesting properties. First, like the ridge estimator, it is a special case of the linear Bayes, mixed and the minimax estimator. Second, it can be expressed as a convex linear combination of the ridge and the least square estimator. Third it is an optimal estimator with a prior mean and dispersion when averaged over Zellner's balanced loss function. Fourth, the Liu estimator, the ridge regression estimator and the least square estimator are all special cases. The relevant optimization problems, prior assumptions and the resulting estimators will be presented in this article.