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MINIMAX REGRET TREATMENT CHOICE WITH INCOMPLETE DATA AND MANY TREATMENTS

Published online by Cambridge University Press:  06 December 2006

Jörg Stoye
Affiliation:
New York University

Abstract

This note adds to the recent research project on treatment choice under ambiguity. I generalize the Manski (Journal of Econometrics, in press) analysis of minimax regret treatment choice by considering a more general setting and, more importantly, by solving for the treatment rule given finitely many (as opposed to two) treatments. The most interesting finding is that with three or more undominated treatments, the minimax regret treatment rule may assign the same treatment to all subjects; thus, the most salient feature of the two-treatment case does not generalize.I thank Chuck Manski, the co-editor, and especially an anonymous referee for helpful comments. Financial support through the Robert Eisner Memorial Fellowship, Department of Economics, Northwestern University, in addition to a Dissertation Year Fellowship, The Graduate School, Northwestern University, is gratefully acknowledged.

Type
NOTES AND PROBLEMS
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Bergemann, D. & K.H. Schlag (2005) Robust Monopoly Pricing: The Case of Regret. Discussion paper, Yale University and European University Institute.
Brock, W.A. (2004) Profiling Problems with Partially Identified Structure. Discussion paper, University of Wisconsin-Madison.
Manski, C.F. (2003) Partial Identification of Probability Distributions. Springer-Verlag.
Manski, C.F. (2004) Statistical treatment rules for heterogeneous populations. Econometrica 72, 12211246.Google Scholar
Manski, C.F. (in press) Minimax-regret treatment choice with missing outcome data. Journal of Econometrics.
Schlag, K.H. (2003) How to Minimize Maximum Regret under Repeated Decision-Making. Discussion paper, European University Institute.
Stoye, J. (2005a) Minimax Regret Treatment Choice with Finite Samples. Discussion paper, New York University.
Stoye, J. (2005b) Statistical Decisions under Ambiguity. Discussion paper, New York University.
Walley, P. (1991) Statistical Reasoning with Imprecise Probabilities. Chapman and Hall.
Wasserman, L. & J.B. Kadane (1992) Computing bounds on expectations. Journal of the American Statistical Association 87, 516522.Google Scholar