Minimal Sufficiency and Completeness for Dichotomous Quantal Response Models

Abstract

Minimal sufficiency and completeness are examined for the multistage, multihit and Weibull quantal response models. It is shown that the response counts are minimal sufficient statistics and conditions are presented for completeness for the families of these models. These results provide an example of a complete sufficient statistic for a curved exponential family which is of higher dimension than the parameter space. Uniformly minimum variance unbiased (UMVU) estimators may not exist for the probability of response at a given dose if the response counts are not complete sufficient statistics.