A Minimax Procedure for Choosing between Two Populations Using Sequential Sampling
利用序贯抽样在两个总体间选择的极小极大程序AI 解读 ↓
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利用序贯抽样在两个总体间选择的极小极大程序
- 研究问题
- 在两个正态总体间作选择时，如何权衡获取信息的抽样成本与选错总体的损失，并确定相应的序贯抽样办法？
- 方法与思路
- 作者使用Wald的极小极大程序，假定总体方差已知且相等，并将错误选择的成本设为均值差乘以反映用途的系数。
- 材料陈述的贡献
- 摘要称所得序贯程序在所有均值差下比固定样本量程序损失更小，并在与所比较双样本程序的比较中通常有所改进。
- 阅读关注点
- 应核对抽样成本与损失函数、停止和选择规则，以及与固定样本量和双样本程序比较时参数与成本是否一致。
- 阅读边界
- 仅据所给Crossref摘要，损失比较受已知等方差及特定成本设定约束，不能推断对未知方差或其他损失函数仍成立。
原文摘要
Summary When a choice has to be made in favour of one of two populations the cost of sampling (experimenting) in order to obtain information on which to base the decision must be balanced against the cost of making the wrong choice. Wald’s (1950) minimax procedure is used to determine a sequential method of sampling when a decision is to be made between two normal populations on the basis of their sample means. It is assumed that the cost of making a wrong choice is given by the difference of the population means multiplied by a factor representing the use made of the chosen population. The population variances are taken as known and equal. It is found that this determines a sequential procedure defined by the ratio of the difference it is desired to detect to a function of the probability with which it is desired to detect that difference, therefore corresponding to a range of tests in which these constants are fixed for the statistician by the user of the results. The performance of this procedure is compared with that for a fixed sample size and found to result in smaller losses over all values of the difference between the populations. A comparison is also made with the double sample procedure of Grundy et al. (1956) on which it is also generally an improvement.