【作者】 王海贤；

【导师】 陈桂景；

【作者基本信息】 安徽大学 ， 概率统计， 2002， 硕士

【摘要】 本文主要讨论具任给精确度(区间长度)和可靠度(覆盖概率)的区间估计问题。精确度与可靠度是区间估计理论中互相矛盾的两个方面，寻找同时满足精确度与可靠度的区间估计在实际应用中具有重要价值。为达到这一目的，往往必须采用序贯抽样的方法。 本文探讨2个主题：两步抽样与纯序贯抽样，从有限步到纯序贯，这2个主题运用不同的手段丰富了序贯区间估计的研究内容。 当分布族满足一定条件时，用两步抽样即可获得具有预先给定长度与覆盖概率的置信区间。在第1章里，作者首先研究了正态总体方差的两步置信区间，并用数值计算的方法给出了第一步的最优抽样量，且证明了固定样本抽样的不存在性。接着，作者构造了更一般的位置刻度族中位置参数与刻度参数的两步区间估计，进一步，作者讨论了正态线性模型中回归系数的相应问题，分别设计了Bonferroni，Scheffe和最大模t_两步区间估计。 两步抽样，只有一次机会利用样本信息决定今后计划，采用纯序贯则可使平均抽样次数节省，另外，在一定的分布族中必须采用纯序贯才能取得满足要求的区间估计。在第2章里，作者首先采用纯序贯抽样，获得线性回归系数的置信域，这可视为Gleser(1965)工作的继续。紧接着，作者把注意力转移到线性模型误差方差的纯序贯区间估计。最后，考虑了一般分布分位点的纯序贯区间估计。以上三种情况，本章证明了当区间长度趋于零时抽样的渐近相容性与渐近有效性。更多还原

【Abstract】 This thesis mainly investigate the problem of confidence intervals of prescribed precision (e.g.,the intervals’ width ) and prescribed reliability controlled by coverage probability. Precision and reliability are two contradictory aspects of the theory of interval estimates. To find a confidence interval of prescribed width and prescribed probability is of groat importance in practical applications, arid thereby sequential procedures have to be employed in many cases.Here, Two topics: two-stage and pure sequential procedures are probed into. From finite to pure sequential steps, the two enrich sequential interval estimates by different means.When the family of distributions satisfy some conditions, the confidence intervals of prescribed width and prescribed coverage probability could be obtained by two-stage procedures. In chapter 1, the author first study the two-stage confidece intervals for the variance of a normal distribution, then work out the optimal sample size of the first stage by numerical computations and establish a proof for the non-existence of fixed-size sampling. Next, the author construct the two-stage confidece intervals for the parameters of the more general location and scale family. Further, the author discuss the correspondent problem in normal linear models, design Bonferroni, Scheffe and the maximum modulus t.two-stage confidence intervals respectively.Two-stage sampling has only one chance of using the information provided by samples to determine the following plan. Pure sequential sampling, however, could use sampling size sparingly. In addition, in some cases, pure sequential procedures have to be applied to acquire the confidence intervals which meet the demands. In chapter 2, first the author adopt pure sequential approach to gain cofidence bounds for linear regression parameters, which could be regarded as the continuations of the work of Gle.ser(1965). After that, the author focus his attention on the pure sequential confidence for the error variance in linear models. Finally, the pure sequential confidence for the quantilo are considered. This chapter has proved the sampling methods in above three cases are asymptotically consistent and asymptotically efficient as the width goes to zero.更多还原