An algorithm for calculating Γ-minimax decision rules under generalized moment conditions

• 成果类型: Article
• 署名作者: Noubiap, RF; Seidel, W
• 署名单位: Helmut Schmidt University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1094-1116
• 关键词: robust bayesian-analysis

摘要

We present an algorithm for calculating a Gamma -minimax decision rule, when Gamma 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.