Liu and Ridge Estimators-A Comparison

ISSN： 0361-0926

Source： Communications in Statistics: Theory and Methods, Vol.41, Iss.20, 2012-10, pp. : 3739-3749

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Abstract

Liu (1993) proposed an estimator that is similar in form but different from the ridge regression estimator of Hoerl and Kennard. More recently, Ozkale and Kaciranlar (2007) 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 estimators. Second, it can be expressed as a convex linear combination of the ridge and the least square estimators. Third, it is an optimal estimator given a prior mean and dispersion when averaged over Zellner's balanced loss function. Fourth, the Liu estimator, ridge regression estimator, and least square estimator are all special cases. The relevant optimization problems, prior assumptions, and the resulting estimators and a comparison of their efficiencies will be presented in this article.