Further investigations of Berkson's example

Abstract

Berkson's bioassay problem is investigated in detail. In addition to maximum likelihood estimators and Berkson's proposed minimum logit χ² estimators, several modified estimators are considered. Two Rao-Blackwellized estimators - a conditional mean and conditional median, given the sufficient statistics - as well as Amemiya's bias-corrected and partially bias-correct estimators are included. The estimators are compared with respect to bias, variance, mean squared error, and Pitman's measure of closeness. The experiment is examined at four different levels of the parameters, and is re-examined subject to a monotonicity condition imposed on the sample space. The results provide a new insight into the controversy over the comparison of minimum χ² and maximum likelihood estimators.