Abstract
Minimax regret (Savage, Journal of the American Statistical Association 46, 55–67, 1951) is the principle of optimizing worst-case loss relative to some measure of unavoidable risk. In statistical decision theory, it provides a non-Bayesian alternative to minimax. It differs from minimax by fulfilling von Neumann–Morgenstern independence but exhibiting menu dependence. Minimax regret has seen occasional use in statistics, and implausible implications of minimax in certain economic problems recently led to its reconsideration by economists.
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Bergemann, D., and K.H. Schlag. 2007. Robust monopoly pricing, Cowles Foundation Discussion Paper 1527R. New Haven: Yale University.
Bergemann, D., and K.H. Schlag. 2008. Pricing without priors. Journal of the European Economic Association (Papers and Proceedings) 6: 560–569.
Berger, J.O. 1985. Statistical decision theory and Bayesian analysis, 2nd ed. New York: Springer.
Borodin, A., and R. El-Yaniv. 1998. Online computation and competitive analysis. Cambridge/New York: Cambridge University Press.
Brock, W.A. 2006. Profiling problems with partially identified structure. Economic Journal 92: F427–F440.
Canner, P.L. 1970. Selecting one of two treatments when the responses are dichotomous. Journal of the American Statistical Association 65: 293–306.
Cesa-Bianchi, N., and G. Lugosi. 2006. Prediction, learning, and games. Cambridge: Cambridge University Press.
Chamberlain, G. 2000. Econometrics and decision theory. Journal of Econometrics 95: 255–283.
Chernoff, H. 1954. Rational selection of decision functions. Econometrica 22: 422–443.
Das Gupta, A., and W. Studden. 1991. Robust Bayesian experimental designs in normal linear models. Annals of Statistics 19: 1244–1256.
Droge, B. 1998. Minimax regret analysis of orthogonal series regression estimation: Selection versus shrinkage. Biometrika 85: 631–643.
Eozenou, P., J. Rivas, and K.H. Schlag. 2006. Minimax regret in practice: Four examples on treatment choice. Discussion paper. Florence: European University Institute.
Foster, D., and R. Vohra. 1999. Regret in the on-line decision problem. Games and Economic Behavior 29: 7–36.
Hannan, J. 1957. Approximation of Bayes risk in repeated play. In Contributions to the theory of games, vol. III, ed. M. Dresher, A.W. Tucker, and P. Wolfe. Princeton: Princeton University Press.
Hansen, B.E. 2005. Exact mean integrated squared error of higher-order kernels. Econometric Theory 21: 1031–1057.
Hart, S., and A. Mas-Colell. 2001. A general class of adaptive strategies. Journal of Economic Theory 98: 26–54.
Hayashi, T. 2008. Regret aversion and opportunity-dependence. Journal of Economic Theory 139: 242–268.
Hirano, K., and J. Porter. 2008. Asymptotics for statistical treatment rules. Discussion paper. Tucson: University of Arizona.
Manski, C.F. 2004. Statistical treatment rules for heterogeneous populations. Econometrica 72: 1221–1246.
Manski, C.F. 2007. Minimax-regret treatment choice with missing outcome data. Journal of Econometrics 139: 105–115.
Manski, C.F. 2008. Identification for prediction and decision. Cambridge, MA: Harvard University Press.
Milnor, J. 1954. Games against nature. In Decision processes, ed. R.M. Thrall, C.H. Coombs, and R.L. Davis. New York: Wiley.
Parmigiani, G. 1992. Minimax, information and ultrapessimism. Theory and Decision 33: 241–252.
Savage, L.J. 1951. The theory of statistical decision. Journal of the American Statistical Association 46: 55–67.
Savage, L.J. 1954. The foundations of statistics. New York: Wiley.
Schlag, K.H. 2003. How to minimize maximum regret in repeated decisions. Discussion paper. Florence: European University Institute.
Schlag, K.H. 2007. Eleven: Designing randomized experiments under minimax regret. Discussion paper. Florence: European University Institute.
Stoye, J. 2006. Statistical decisions under ambiguity. Discussion paper. New York: New York University.
Stoye, J. 2007a. Minimax regret treatment choice with incomplete data and many treatments. Econometric Theory 23: 190–199.
Stoye, J. 2007b. Axioms for minimax regret choice correspondences. Discussion paper. New York: New York University.
Stoye, J. 2007c. Minimax regret treatment choice with finite samples and missing outcome data. In Proceedings of the fifth international symposium on imprecise probability: Theories and applications, ed. G. de Cooman, J. Veinarová, and M. Zaffalon. Prague.
Stoye, J. 2007d. Minimax regret treatment choice with finite samples. Discussion paper. New York: New York University.
Stoye, J. 2009. Minimax regret treatment choice with missing data: An application to young offenders. Journal of Statistical Theory and Practice, forthcoming.
Wald, A. 1950. Statistical decision functions. New York: Wiley.
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Stoye, J. (2018). Minimax Regret. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2965
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2965
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