Ridge Estimation of Independent Poisson Means under Entropy Loss

Abstract

Hoerl and Kennard (1970) originally introduoed ridge estimators for multiple linear regression model. The resulting ridge estimators can be developed from a Bayesian viewpoint by assuming a suitable conjugate normal prior. A similar phenomenon occurs in the Poisson case when one defines the distance between two points as the entropy distance rather than the Euclidean norm. Three basic properties of ridge type estimators of independent Poisson means, as advocated by Hoerl and Kennard (1970), will be derived in this paper. The ridge estimators derived by using improper hierarchical priors under entropy loss can be shown to be admissible. Also the conditions of ridge estimators dominating the generalized Bayes estimators are given in this paper. In addition, Monte Carlo simulations are undertaken to show the risk dominance. Finally, the RSL approach will be employed to compare the ridge estimators with the generalized Bayes estimators including some standard estimators in terms of their Bayes risk performance. HoerZ and Kennard (1970) originally introduced ridge. © R. Oldenbourg Verlag, München 1992