Generalizations of Steel's Treatments-Versus-Control Multivariate Sign Test
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Steel 多处理对照多元符号检验的推广
- 研究问题
- 在随机区组设计中，如何允许对照重复出现、各处理出现次数不等，并同时比较多个处理与对照的差异？
- 方法与思路
- 作者推广 Steel 多元符号检验，提出符号处理对照平衡设计，并用适合同时推断的 Pitman 渐近相对效率选择设计。
- 材料陈述的贡献
- 摘要称，作者找到该设计类中的渐近最优方案，说明参数与非参数分析的最优设计不同，并提供同时置信陈述。
- 阅读关注点
- 应核对设计类的约束、同时推断所用效率准则、最优性的比较范围，以及处理对照差异置信陈述的成立条件。
- 阅读边界
- 仅据所给 OpenAlex 索引摘要，稿件版本未注明；摘要未说明最优设计的具体配置和分布条件，也未给出因果识别框架。
原文摘要
Steel (1959) introduced a nonparametric multivariate sign test to allow one to compare p ≥ 2 test treatments simultaneously with a control or standard treatment in a randomized-block setting. Steel proposed using blocks of size p + 1 composed of one observation from each treatment. Intuitively, it seems that the control should be observed more often that a test treatment, because the control is involved in all treatment-control comparisons and an individual test treatment is involved in only one. Studies in the corresponding parametric analyses bear out this intuition. In this article Steel's multivariate sign test is generalized to allow the control to appear more than once in each block and to allow the test treatments to appear an unequal number of times in each block. A class of block designs known as sign-treatment-control balanced designs is proposed. This class is a counterpart of the classes of supplemented balance designs and balanced-treatment incomplete block designs that have been popular for parametric treatment-control comparisons. Using a modification of Pitman asymptotic relative efficiency appropriate for simultaneous inference, an asymptotically optimal design in this new class is found. Asymptotically optimal designs for the parametric and nonparametric analyses are shown to differ. Nonparametric simultaneous confidence statements for all treatment-control differences are presented.