Minimax-regret treatment rules with many treatments

Matthew Masten

The Japanese Economic Review, 2023, vol. 74, issue 4, No 4, 537 pages

Abstract: Abstract Statistical treatment rules map data into treatment choices. Optimal treatment rules maximize social welfare. Although some finite sample results exist, it is generally difficult to prove that a particular treatment rule is optimal. This paper develops asymptotic and numerical results on minimax-regret treatment rules when there are many treatments. I first extend a result of Hirano and Porter (Econometrica 77:1683–1701, 2009) to show that an empirical success rule is asymptotically optimal under the minimax-regret criterion. The key difference is that I use a permutation invariance argument from Lehmann (Ann Math Stat 37:1–6, 1966) to solve the limit experiment instead of applying results from hypothesis testing. I then compare the finite sample performance of several treatment rules. I find that the empirical success rule performs poorly in unbalanced designs, and that when prior information about treatments is symmetric, balanced designs are preferred to unbalanced designs. Finally, I discuss how to compute optimal finite sample rules by applying methods from computational game theory.

Keywords: Statistical decision theory; Statistical treatment choice; Empirical welfare maximization (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42973-023-00147-0

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