Studies on the optimality of methods of statistical sequential decisions

统计序贯决策方法的最优性研究

• 批准号: 11640106
• 负责人: ISOGAI Eiichi
• 金额: $ 2.18万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640106/
• 关键词: sequential estimation; stopping rule; regret; biased-corrected; second-order asymptotic expansion; minimum risk; bounded risk; point estimation; パーセンタイル; 正規分布; 一様可積分; 指数分布

Head investigator and each of the investigators obtained the research results concerning the title of this project directly or indirectly. The main results by head investigator are as follows :(1) We considered the problem of estimating a linear combination of unknown location and scale parameters of a negative exponential distribution. Given a class of estimators, we want to estimate the linear combination by using the sample of the smallest size such that the risk associated with them is not greater than a preassigned error bound. We proposed a sequential estimator and obtained the asymptotic expansion of the risk.(2) We considered the sequential point estimation problem of a linear combination of means of k populations. Our procedure was shown to have asymptotically less risk when compared with the existing procedure for some class of distributions.(3) We considered the sequential point estimation problem of a linear combination of unknown mean and standard deviation of a normal distribution under squared relative error plus linear cost as a loss function. We proposed a class of estimators and obtained second-order asymptotic expansions of the risk associated with the corresponding sequential estimators.

课题组长及各研究者直接或间接获得了与本项目名称相关的研究成果。首席研究员的主要结果如下：（1）我们考虑了估计负指数分布的未知位置和尺度参数的线性组合的问题。给定一类估计量，我们希望通过使用最小尺寸的样本来估计线性组合，以便与它们相关的风险不大于预先分配的误差范围。我们提出了序贯估计器并得到了风险的渐近展开。(2)考虑了k个总体均值线性组合的序贯点估计问题。与某些类别的分布的现有程序相比，我们的程序被证明具有渐近更小的风险。（3）我们考虑了在平方相对误差加上正态分布的未知均值和标准差的线性组合的序贯点估计问题作为损失函数的线性成本。我们提出了一类估计量，并获得了与相应顺序估计量相关的风险的二阶渐近展开式。

项目成果

Akahira Masafumi: "On the normalized deficiency of estimators"Metron. vol. 57, no. 3&4. 25-34 (1999)

Akahira Masafumi：“论估计量的标准化缺陷”Metron。

Masafumi Akahira: "The higher order large-deviation approximation for the distribution of the sum of independent discrete random variables"Communications in Statistics-Theory and Methods. 28・3&4. 705-726 (1999)

Masafumi Akahira：“独立离散随机变量之和的分布的高阶大偏差近似”通讯统计理论与方法 28・3&4（1999）。

Keiji Izuchi: "Singular inner functions of L'-type"Journal of Korean Mathematical Society. 36・4. 787-811 (1999)

Keiji Izuchi：“L型的奇异内函数”韩国数学会杂志 36・4（1999）。

Akahira Masafumi: "The concept of normalized deficiency and its applications"Statistics & Decisions. vol. 17. 403-411 (1999)

赤平雅文：“标准化缺陷的概念及其应用”统计

Shigeo Akashi: "An entropy theoretic inversion formula for the distribution of proper values of a compact positive operator"Open Systems and Information Dynamics. 6. 303-308 (1999)

Shigeo Akashi：“紧凑正算子真值分布的熵理论反演公式”开放系统和信息动力学。