## The Annals of Statistics

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

### 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 $\bar{w}$.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

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**

links.jstor.org

**Keywords**

G2E20 G2L12 Asymptotic normal distribution binary response Markov chain peaks and valleys up-and-down method Wetherill's estimator $\bar{w}$

#### Citation

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