Asymptotic Properties of $\bar{w}$, an Estimator of the ED50 Suggested for Use in Up-and-Down Experiments in Bio-Assay

Abstract

Wetherill's estimator $\bar{w}$ is asymptotically equivalent to the mean of peaks and valleys in the sequence of responses in an up-and-down experiment. The asymptotic distribution of $\bar{w}$ is derived and the asymptotic variance expression is simplified. Some values of asymptotic means and variances are calculated for logistic response. They are compared with analogous values for the estimator suggested by Dixon and Mood. These estimators are also compared by some computer simulation. For the conditions investigated, Dixon and Mood's estimator is to be preferred to $\bar{w}$.