Optimal relevant subset designs in nonlinear models

It is well known that certain ancillary statistics form a relevant subset, a subset of the sample space on which inference should be restricted, and that conditioning on such ancillary statistics 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 experiments has not been well characterized. Ancillary statistics are not known prior to data collection and as a result cannot be incorporated into the design a priori. Conversely, in sequential experiments the ancillary statistics based on the data from the preceding observations are known and can be used to determine the design assignment of 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 adaptive designs.