Small-Sample Quantal Response Methods for Estimating the Location Parameter for a Location-Scale Family of Dose-Response Curves

Abstract

When one uses a small number of quantal responses to estimate a location parameter in the presence of an unknown scale parameter for a logistic or normal dose-response curve, it is often possible to substantially improve upon the method of maximum likelihood. Some generalized method-of-moments estimators are proposed for an arbitrary dose-response curve known up to location and scale and a theorem is given that establishes existence and uniqueness properties. In a computer study of the exact distributions of these estimators, they proved to be far superior to maximum likelihood and minimum logit chi-squared estimators of location in the logistic case.