Shrinkage Estimators of Relative Potency

Abstract

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all finite sample sizes. Furthermore, it is shown that this estimator asymptotically behaves the same as the usual maximum likelihood estimator.

Key Words:

• Asymptotic distribution
• Bayesian
• Frequentist
• Parallel line bioassay
• Relative potency
• Shrinkage estimator