Studies on statistical sequential estimation problems by the method of sequential analysis

用序贯分析方法研究统计序贯估计问题

• 批准号: 18540117
• 负责人: ISOGAI Eiichi
• 金额: $ 2.53万
• 依托单位: Niigata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540117/
• 关键词: fully sequential procedure; stopping rule; sequential confidence interval; normal distribution; exponential distribution; asymptotic consistency; asymptotic expansion; rate of convergence; 正規分布; 収束の速さ; 非線形再生理論; 指数分布

Head investigator and each of investigators obtained the results which are concerned with the title of this project directly or indirectly. The main results given by head investigator are as follows.(1) We consider the sequential fixed-width confidence interval estimation problem for a function of unknown location and scale parameters of a negative exponential distribution. We propose a fully sequential procedure and construct sequential confidence intervals for the function. Its asymptotic consistency is shown. As an application we consider the problem of the ratio of the parameters and give the second-order asymptotic expansion of the average sample size of the above procedure as the width of confidence interval approaches zero. Some simulation results are presented.(2) We consider the convergence rate of sequential fixed-width confidence intervals for a linear function of unknown mean and standard deviation of a normal distribution. We use the fully sequential procedure proposed by Takada to construct sequential confidence intervals for the linear function and investigate the convergence rate of the coverage probability as the width of the confidence interval approaches zero. We also derive a second-order asymptotic expansion of the average sample size.

课题组长及各位研究者所获得的结果都直接或间接与本项目的名称有关。首席研究员给出的主要结果如下：(1)我们考虑负指数分布的未知位置和尺度参数函数的顺序固定宽度置信区间估计问题。我们提出了一个完全顺序的过程，并为该函数构建了顺序置信区间。证明了其渐近一致性。作为一个应用，我们考虑参数的比率问题，并在置信区间宽度接近零时给出上述过程的平均样本量的二阶渐近展开。给出了一些仿真结果。(2)我们考虑了正态分布的未知均值和标准差的线性函数的顺序固定宽度置信区间的收敛速度。我们使用 Takada 提出的完全序贯过程来构造线性函数的序贯置信区间，并研究当置信区间的宽度接近零时覆盖概率的收敛速度。我们还推导出平均样本量的二阶渐近展开。

项目成果

On the Pitman estimator for a family of non-regular distributions

关于非正则分布族的 Pitman 估计量

• 发表时间: 2007
• 作者: Akahira Masafumi

On generalizing Caristi's fixed point theorem

关于卡里斯蒂不动点定理的推广

• 发表时间: 2007
• 作者: Araya Yousuke

The asymptotic bound by the Kiefer-type information inequality and its attainment

基弗型信息不等式的渐近界及其实现

• 发表时间: 2007
• 作者: Akahira; M.; Ohyauchi; N
• 通讯作者: N

Accelerating the singular value decomposition of rectangular matrices

加速矩形矩阵的奇异值分解

• 发表时间: 2007
• 作者: Yamamoto; Y.; Fukaya; T.; Uneyama; T.; Takata; M.; Kimura; K.; Iwasaki; M; Nakamura; Y
• 通讯作者: Y

On the convergence rate of sequential fixed-width confidence intervals for normal parameters

关于正态参数的顺序固定宽度置信区间的收敛速度

• 发表时间: 2008
• 作者: Isogai; E.; Futschik; A
• 通讯作者: A