Admissible treatment rules for a risk-averse planner with experimental data on an innovation

By Charles F. Manski, Aleksey Tetenov. 2007

48 citations recorded by the source corpus.

Consider a planner choosing treatments for observationally identical persons who vary in their response to treatment. There are two treatments with binary outcomes. One is a status quo with known population success rate. The other is an innovation for which the data are the outcomes of an experiment. Karlin and Rubin [1956. The theory of decision procedures for distributions with monotone likelihood ratio. Ann. Math. Statist. 27, 272–299] assumed that the objective is to maximize the population success rate and showed that the admissible rules are the KR-monotone rules. These assign everyone to the status quo if the number of experimental successes is below a specified threshold and everyone to the innovation if experimental success exceeds the threshold. We assume that the objective is to maximize a concave-monotone function f( ·) of the success rate and show that admissibility depends on the curvature of f( ·). Let a fractional monotone rule be one where the fraction of persons assigned to the innovation weakly increases with the number of experimental successes. We show that the class of fractional monotone rules is complete if f( ·) is concave and strictly monotone. Define an M-step monotone rule to be a fractional monotone rule with an interior fractional treatment assignment for no more than M consecutive values of the number of experimental successes. The M-step monotone rules form a complete class if f( ·) is differentiable and has sufficiently weak curvature. Bayes rules and the minimax-regret rule depend on the curvature of the welfare function. © 2006 Elsevier B.V. All rights reserved.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c71e27f66488e65a2d39a230e49472cd46a56dbf

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Citations in the corpus

Minimax regret treatment choice with finite samples (2009, background): “Minimax regret as a criterion for statistical decisions has recently attracted renewed interest (Brock 2004, Hirano and Porter 2005, Manski 2004, 2005, 2006a, 2006b, Schlag 2006, Stoye 2006a).”
Minimax regret treatment choice with covariates or with limited validity of experiments (2012, methodology): “One recent focus of Charles Manski’s research is to apply statistical decision theory, and in particular the minimax regret criterion, to problems of treatment choice (Manski (2000, 2004, 2006, 2007a, 2007b, 2009); Brock and Manski (2008)).”
Statistical treatment choice based on asymmetric minimax regret criteria (2009, unknown): “(10) ̄̄̄̄ ̄ Ã √  p  [ (1)] Ã 1   X”