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雷达卡
摘要翻译：
在具有正态误差的单因素方差分析标准下，假设处理均值在因子水平上不降低，提出了一种新的估计处理均值的算法--逐步下降最大均值选择算法(SDMMSA)。我们证明了i）SDMMSA和Pooled Nearch Violator算法(PAVA)（在许多问题中广泛使用的算法）对正规均值产生相同的估计量，ii)估计量是MLE的，并且iii）每个估计量的分布在每个处理方法中都是随机不减的。作为这种随机排序的应用，在单调治疗（剂量）平均的假设下，建立了识别最小有效剂量(MED)的零假设序列。建立了一种在强意义上控制实验误差率的逐级测试程序。当MED=1时，所提出的检验比Hsu和Berger(1999)的检验都强。
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英文标题：
《An Algorithm to Estimate Monotone Normal Means and its Application to
Identify the Minimum Effective Dose》
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作者：
Weizhen Wang and Jianan Peng
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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).
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PDF链接：
https://arxiv.org/pdf/801.0079
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