Nonparametric estimators of the mean tolerance in bioassay

Theoretical properties of the Spearman-Kärber estimator of the mean tolerance in a quantal response bioassay are discussed, and its limiting distribution is studied under three different limiting processes. The Reed-Muench and Dragstedt-Behrens estimators are shown to be estimators of the mean, not the median, tolerance and to be nearly equivalent to the Spearman-Kärber estimator. The limiting distributions of the Reed-Muench estimator are considered in detail.