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Biometrika 1976 63(3):621-626; doi:10.1093/biomet/63.3.621
© 1976 by Biometrika Trust
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Some properties of Spearman-type estimators of the variance and percentiles in bioassay

JOSEPH J. CHMIEL

Department of Statistics, Stanford University California

Theoretical results for the Spearman-type variance estimator in the quantal response bioassay problem are determined when the mean of the underlying tolerance distribution is known, and also when it is unknown. For an experiment with infinitely many dose levels, the estimator is proved to be finite with probability one, and its mean and variance are given. Allowing the dose interval to approach zero, the estimator is shown to be asymptotically normal and asymptotically highly efficient. Similar asymptotic findings are also reached for a Spearman-type percentile estimator. The results approximate the performance of Spearman-type estimators in most practical situations and argue for their use.

Key Words: Bioassay • Nonparametric estimator • Percentile • Quantal response • Spearman-type • Variance


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