Fisher (1934) argued that certain ancillary statistics form a relevant subset, a subset of the sample space on which inference should be restricted, and showed that conditioning on their observed value reduces the dimension of the data without a loss of information. The use of ancillary statistics in post-data inference has received significant attention; however, their role in the design of the experiment has not been well characterized. Ancillary statistics are unknown prior to data collection and as a result cannot be incorporated into the design a priori. However, if the data are observed sequentially then the ancillary statistics based on the data from the preceding observations can be used to determine the design assignment for the current observation. The main results of this work describe the benefits of incorporating ancillary statistics, specifically, the ancillary statistic that constitutes a relevant subset, into an adaptive design.
翻译:Fisher(1934年)(1934年)认为,某些辅助统计构成一个相关的子集,即应限制推断的抽样空间的子集,并表明,以其观察到的价值为条件,可以减少数据的范围,而不会丢失信息;在数据后推论中使用辅助统计的做法受到极大注意;然而,在设计实验时,它们的作用没有很好地说明;辅助统计在数据收集之前是未知的,因此不能先验地纳入设计中;然而,如果按顺序观察数据,然后可以使用基于前述观测结果的数据的辅助统计来确定当前观测的设计任务;这项工作的主要结果说明将辅助统计,特别是构成相关子集的辅助统计纳入适应性设计的好处。