【作者】 李艳；

【导师】 濮晓龙；

【作者基本信息】 华东师范大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 自Wald(1947) 提出序贯概率比检验(Sequential Probability Ratio Test,以下简称“SPRT”)方法以来,序贯方法逐渐成为解决假设检验问题的重要工具.SPRT方法具有许多优良的性质,是序贯假设检验中常用的方法.现在,许多学者采用两次SPRT方法来解决一个假设检验问题。他们的想法和处理方法都有许多可取之处,也得到了一些比较好的缔果。本文将对这类问题进行总结,并对参数选择和方案设计提出新的解决方法。目前的序贯分析研究中,有两个假设检验问题涉及到了两次SPRT方法。第一个是简单假设检验问题。为使平均样本量在某个真参数下达到最小,Lorden(1976) 首先采用两次SPRT方法(称作“2-SPRT方法”)来解决该问题。在指数型分布族下,2-SPRT方案的判断准则在图形上是两条相交直线。Lorden、Huffman、陈家鼎都证明了2-SPRT方法的渐近有效性。本文讨论了方差已知的正态分布均值的简单假设检验问题下,2-SPRT方法中参数的选择问题,提出了参数选择的新方法--通过求解方程来选择参数。例子的结果显示,本文方法的效果是比较好的。此外,从实际问题的需要出发,本文还首先提出了截断2-SPRT方法(即在2-SPRT方案基础上设置最大样本量)并解决了该方法下参数的选择问题。第二个是双边假设检验问题。为满足实际需要,许多学者将双边假设检验问题转化为三个假设的检验问题,并采用两次SPRT方法来解决该问题.当双边假设检验问题转化为三个假设的检验问题时,需确定假设中的两个参数,但目前尚无人对参数的选择问题作过研究。本文采用求解方程组的方法来设计参数、制定两次SPRT抽样检验方案,从例子的结果来看,本文方法的效果是比较好的。更多还原

【Abstract】 Since Wald(1947) proposed method of Sequential Probability Ratio Test (SPRT), SPRT has become an important tool for solving hypothesis test problems. It has so many excellent properties that it has been used widely.Some scholars developed new methods to solve a hypothesis test problem — using SPRT twice. In some degree, their ideas and methods are proper and some ideal results have been gotten. In this paper, these methods are summed up and new methods are developed, including parameters selection and the design of hypotheses.At present, there are two hypothesis test problems involved in Two SPRTs in sequential analysis research.The first one is simple hypothesis test problem. To reduce average sample number at some point, Lorden (1976) proposed the method of 2-SPRT, i.e. to use SPRT twice. Lorden, Huffman and Chen Jiading have proved that 2-SPRT is asymptotically efficient. In this paper, in symmetric normal case, a new method is used to select parameters of 2-SPRT by solving equation. Examples show that this method is quite applicable and efficient. Additionally, a new method of truncated 2-SPRT is put up in this paper.The second one is two-sided hypothesis test problem. To satisfy practical needs, many scholars turned two-sided hypothesis test problem into three hypotheses one byadding two proper hypothesis parameters, and used the method of two SPRTs to solve it. These hypothesis parameters, which have never been discussed before, are found in some requires also by solving equations. Only symmetric test of normal mean with variance known is considered here.更多还原