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Efficient sequential designs with binary data. (English) Zbl 0588.62133
New sequential designs are proposed for efficient estimation of the percentiles of a quantal response curve for small- or moderate-sized experiments. The sequential designs are constructed on a parametric model for the response curve, whose parameters are estimated by using all of the data available, and the next design point is determined from the estimated quantal response curve (EQRC).
The logit-MLE version of the proposed designs, using a two-parameter logistic model and the maximum likelihood method for parameter estimation, is shown heuristically to be a natural analogue of the Robbins-Monro (RM) procedure. Under consistency assumptions, it is shown to be asymptotically optimal as it is asymptotically equivalent to an adaptive RM procedure.
Comparative simulation studies are carried out for the logit-MLE version of the sequential design with truncation, the adaptive RM design with truncation and the nonadaptive RM design, and indicate the proposed MLE designs to be useful alternatives to the standard ones. A nonparametric sequential design, via the Spearman-Kärber estimator, for estimating the median is also proposed.
Reviewer: K.Uosaki

MSC:
62L05 Sequential statistical design
62L20 Stochastic approximation
62L12 Sequential estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
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