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March, 1985 Asymptotic Properties of $\bar{w}$, an Estimator of the ED50 Suggested for Use in Up-and-Down Experiments in Bio-Assay
Christopher D. Kershaw
Ann. Statist. 13(1): 85-94 (March, 1985). DOI: 10.1214/aos/1176346578

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 $\bar{w}$.

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Christopher D. Kershaw. "Asymptotic Properties of $\bar{w}$, an Estimator of the ED50 Suggested for Use in Up-and-Down Experiments in Bio-Assay." Ann. Statist. 13 (1) 85 - 94, March, 1985. https://doi.org/10.1214/aos/1176346578

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0595.62081
MathSciNet: MR773154
Digital Object Identifier: 10.1214/aos/1176346578

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

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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