Efficient Model-Based Sequential Designs for Sensitivity Experiments.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A sequential design for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all the data available via a parametric model. Its efficiency in terms of saving the number of runs and its robustness against the distributional assumption are demonstrated heuristically and in a simulation study. A linear approximation to the logit-MLE version of the proposed sequential design is shown to be equivalent to an asymptotically optimal stochastic approximation method, thereby providing a large sample justification. For sample size between 12 and 35, the simulation study shows that the logit-MLE version of the general sequential procedure substantially outperforms an adaptive and asymptotically optimal version of the Robbins-Monro method, which in turn outperforms the nonadaptive Robbins-Munro and Up-and-Down methods. A nonparametric sequential design, via the Spearman-Karber estimator, for estimating the median is also proposed. Author
- Statistics and Probability