The VPRT: A Sequential Testing Procedure Dominating the SPRT
The VPRT: A Sequential Testing Procedure Dominating the SPRT
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VPRT：主导 SPRT 的顺序测试程序
DOI：
10.1017/s0266466600007751
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发表时间：
1993
影响因子：
0.8
通讯作者：
P. Morgan
中科院分区：
文献类型：
--
作者：
N. Cressie;P. Morgan
在比序列分析文献中通常做出的更一般的假设下，发现两个简单假设的变样本大小-序列概率比检验（VPRT）在所有序列决策过程中使预期净收益最大化。相比之下，Wald和Wolfowitz提出了序列概率比检验（SPRT）来最小化期望样本量，但他们对决策问题参数的假设是限制性的。在本文中，我们展示了预期净收益最大化的VPRT也最小化了预期（相对于数据和先验）总抽样成本，并且，在比Wald和Wolfowitz施加的条件稍微更一般的条件下，它简化为一次一个观测的序列概率比检验（SPRT）。还研究了VPRT的大小和功率取决于决策问题参数的方式。
Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.