Abstract

The problem of sequential estimation of the mean with quadratic loss and fixed cost per observation is considered within the Bayesian framework. A robust sequential procedure, not depending on the distributions of outcome variables and the prior, in the Bayes sequential estimation is investigated. In the present article, the second-order approximations to the expected sample size and the Bayes risk of the robust sequential procedure are obtained for the arbitrary distributions of outcome variables and the prior. The second-order efficiency is further discussed in an example.

中文翻译：

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贝叶斯顺序估计中鲁棒顺序过程的二阶近似

摘要

在贝叶斯框架内考虑了具有二次损失和每次观测的固定成本的均值顺序估计问题。在贝叶斯顺序估计中，研究了一种不依赖于结果变量和先验分布的稳健顺序过程。在本文中，对于结果变量和先验变量的任意分布，可以获得预期样本量的二阶近似值和鲁棒顺序过程的贝叶斯风险。实例中将进一步讨论二阶效率。