Improvement ranges for shrinkage estimators with stochastic target

Abstract

Shrinkage estimators often have a biasing parameter (saym k) and a non-stochastic shrinkage target (zero). Range of stochastic k values in which the mean squared error (MSE) of ordinary least squares estimator (OLS) is reduced is known and tabulated invinod and Ullah (1981, p. 218). This paper generalized these ranges for Bayesian and non-Bayesian estimators involving stochastic shrinkage targets. For example, the shrinkage target is the avarage of the regression coefficients in Lindley and Smith (1972) and Zellner and Vandaele (1975). Also included are results on Bayes-Almon estimator for the distributed lag models and certain iterative estimators. Interstingly, Lindley and Smith's iterative ridge estimator is shown to be no better than their first stage estimator.

Keywords:

• regression
• biased
• ridge
• Stein-rule
• mean squared error matrix
• mean squared error matrix
• shrinkage toward stochastic target