Optimal Relevant Subset Designs in Nonlinear Models

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.