标题： 一种估计单调正态均值的算法及其在识别最小有效剂量中的应用 显示英文标题

标题： An Algorithm to Estimate Monotone Normal Means and its Application to Identify the Minimum Effective Dose

摘要： 在一元方差分析（ANOVA）的标准设定中，当误差服从正态分布且假设处理均值随着因子水平的增加而非递减时，提出了一种新的算法，称为降步最大均值选择算法（SDMMSA），用于估计处理均值。 我们证明了以下几点：i) SDMMSA 和广泛应用的合并相邻违规者算法（PAVA）对正态均值生成相同的估计量；ii) 这些估计量是最大似然估计（MLE）；iii) 每个估计量的分布相对于每个处理均值是非随机递增的。 作为这种随机排序的应用，基于处理均值单调的假设，提出了一个识别最小有效剂量（MED）的一系列零假设。构建了一个逐步上升检验程序，该程序以强意义控制实验错误率。当 MED=1 时，所提出的检验比 Hsu 和 Berger (1999) 的检验更强大。 显示英文摘要

摘要： In the standard setting of one-way ANOVA with normal errors, a new algorithm, called the Step Down Maximum Mean Selection Algorithm (SDMMSA), is proposed to estimate the treatment means under an assumption that the treatment mean is nondecreasing in the factor level. We prove that i) the SDMMSA and the Pooled Adjacent Violator Algorithm (PAVA), a widely used algorithm in many problems, generate the same estimators for normal means, ii) the estimators are the mle's, and iii) the distribution of each of the estimators is stochastically nondecreasing in each of the treatment means. As an application of this stochastic ordering, a sequence of null hypotheses to identify the minimum effective dose (MED) is formulated under the assumption of monotone treatment(dose) means. A step-up testing procedure, which controls the experimentwise error rate in the strong sense, is constructed. When the MED=1, the proposed test is uniformly more powerful than Hsu and Berger's (1999).