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August 2001 An algorithm for calculating Γ-minimax decision rules under generalized moment conditions
Roger Fandom Noubiap, Wilfried Seidel
Ann. Statist. 29(4): 1094-1116 (August 2001). DOI: 10.1214/aos/1013699995


We present an algorithm for calculating a $\Gamma$-minimax decision rule, when is given by a finite number of generalized moment conditions. Such a decision rule minimizes the maximum of the integrals of the risk function with respect to all distributions in $\Gamma$. The inner maximization problem is approximated by a sequence of linear programs. This approximation is combined with an elimination technique which quickly reduces the domain of the variables of the outer minimization problem. To test for convergence in a final step, the inner maximization problem has to be completely solved once for the candidate of the $\Gamma$-minimax rule found by the algorithm. For an infinite, compact parameter space, this is done by semi-infinite programming. The algorithm is applied to calculate robustified Bayesian designs in a logistic regression model and $\Gamma$-minimax tests in monotone decision problems.


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Roger Fandom Noubiap. Wilfried Seidel. "An algorithm for calculating Γ-minimax decision rules under generalized moment conditions." Ann. Statist. 29 (4) 1094 - 1116, August 2001.


Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1041.62005
MathSciNet: MR1869242
Digital Object Identifier: 10.1214/aos/1013699995

Primary: 62C12
Secondary: 62F35 , 90C34

Keywords: Bayesian robustness , Experimental design , Gamma-minimax decision rules , minimax problems , monotone decision problems , semi-infinite programming

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 4 • August 2001
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