This paper uses the minimax regret criterion to analyze choice between two treatments when one has observed a finite sample that is plagued by missing data. The analysis is entirely in terms of exact finite sample regret, as opposed to asymptotic approximations or finite sample bounds. It thus extends Manski (in press), who largely abstracts from finite sample problems, as well as Stoye (2006a), who provides finite sample results but abtracts from missing data. Core findings are: (i) Minimax regret is achieved by randomizing over two rules that were identified in the aforecited papers. (ii) For every sample size, there exists a sufficiently small (but positive) proportion of missing data such that if less data are missing, the missing data problem is ignored altogether and Stoye's (2006a) results apply. (iii) For every positive fraction of missing data, the value of additional observations drops to zero at a finite sample size. I also provide the decision problem's value function and briefly touch on optimal sample design as well as unknown propensity scores.
Keywords. Minimax regret, missing data, imprecise probability models, statistical decision theory, partial identification, treatment evaluation.
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Department of Economics
19 W. 4th Street
New York, NY 10012
E-mail addresses:
| Joerg Stoye | j.stoye@nyu.edu |
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