Minimax regret treatment choice with finite samples

Joerg Stoye

Abstract:

This paper applies the minimax regret criterion to choice between two treatments conditional on
observation of a finite sample. The analysis is based on exact small sample regret and does not use
asymptotic approximations or finite-sample bounds. Core results are: (i) Minimax regret treatment rules
are well approximated by empirical success rules in many cases, but differ from them significantly 
both in terms of how the rules look and in terms of maximal regret incurred  for small sample sizes
and certain sample designs. (ii) Absent prior cross-covariate restrictions on treatment outcomes, they
prescribe inference that is completely separate across covariates, leading to no-data rules as the support
of a covariate grows. I conclude by offering an assessment of these results.