The use of Previous Experience in Reaching Statistical Decisions
The use of Previous Experience in Reaching Statistical Decisions
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DOI：
10.1007/978-1-4614-1412-4_6
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发表时间：
1952-09
影响因子：
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通讯作者：
J. Hodges;E. Lehmann
中科院分区：
文献类型：
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作者：
J. Hodges;E. Lehmann
而不是最小化的最大风险，它建议限制注意决策程序的最大风险不超过极大极小风险超过一个给定的数额。受此限制，人们可能希望最小化关于先前经验所建议的一些猜测的先验分布的平均风险。它示出如何沃尔德的极大极小理论可以修改，以产生类似的结果，这种限制贝叶斯解决方案。讨论了许多例子，并简要考虑了上述标准的一些扩展。
Instead of minimizing the maximum risk it is proposed to re-strict attention to decision procedures whose maximum risk does not exceed the minimax risk by more than a given amount. Subject to this restriction one may wish to minimize the average risk with respect to some guessed a priori distribution suggested by previous experience. It is shown how Wald’s minimax theory can be modified to yield analogous results concerning such restricted Bayes solutions. A number of examples are discussed, and some extensions of the above criterion are briefly considered.