Efficient Sequential Designs With Binary Data
提出一类用于估计分位数反应曲线百分位数的序贯设计，基于参数模型高效汇总数据，并证明其渐近一致性、最优性和非参数性，模拟显示小样本下表现良好。
Abstract A class of sequential designs for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all of the data available via a parametric model. The logit-MLE version of the proposed designs can be viewed as a natural analog of the Robbins—Monro procedure in the case of binary data. It is shown to be asymptotically consistent, optimal, and nonparametric via its connection with the latter procedure. For certain choices of initial designs, the proposed method performs very well in a simulation study for sample sizes up to 35. A nonparametric sequential design, via the Spearman—Kärber estimator, for estimating the median is also proposed.