Why randomize? Minimax optimality under permutation invariance

Yuehao Bai

Journal of Econometrics, 2023, vol. 232, issue 2, 565-575

Abstract: This paper studies finite sample minimax optimal randomization schemes and estimation schemes in estimating parameters including the average treatment effect, when treatment effects are heterogeneous. A randomization scheme is a distribution over a group of permutations of a given treatment assignment vector. An estimation scheme is a joint distribution over assignment vectors, linear estimators, and permutations of assignment vectors. The key element in the minimax problem is that the worst case is over a class of distributions of the data which is invariant to a group of permutations. First, I show that given any assignment vector and any estimator, the uniform distribution over the same group of permutations, namely the complete randomization scheme, is minimax optimal. Second, under further assumptions on the class of distributions and the objective function, I show the minimax optimal estimation scheme involves completely randomizing an assignment vector, while the optimal estimator is the difference-in-means under complete invariance and a weighted average of within-block differences under a block structure, and the number of treated units is determined by the Neyman allocation.

Keywords: Experimental design; Permutation invariance; Minimax optimality; Average treatment effect (search for similar items in EconPapers)
JEL-codes: C13 C90 C93 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:232:y:2023:i:2:p:565-575

DOI: 10.1016/j.jeconom.2021.10.009

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