## The Annals of Statistics

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

Christopher D. Kershaw

#### 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 $\bar{w}$.

#### Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 85-94.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346578

Digital Object Identifier
doi:10.1214/aos/1176346578

Mathematical Reviews number (MathSciNet)
MR773154

Zentralblatt MATH identifier
0595.62081

JSTOR
Kershaw, Christopher D. Asymptotic Properties of $\bar{w}$, an Estimator of the ED50 Suggested for Use in Up-and-Down Experiments in Bio-Assay. Ann. Statist. 13 (1985), no. 1, 85--94. doi:10.1214/aos/1176346578. https://projecteuclid.org/euclid.aos/1176346578