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Studies on.the structure of.methods, of.sequential estimation

序贯估计方法结构的研究

基本信息

批准号：
14540107
负责人：
ISOGAI Eiichi
金额：
$ 2.3万
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：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540107/
关键词：
sequential estimation fully sequential procedure power of scale parameter bounded risk normal distribution exponential distribution second-order asymptotic expansion bias adjustment 停止規則尺度母数リグレット最小危険逐次手法

项目摘要

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 consider the point estimation problem of the powers of a standard deviation of a normal distribution with unknown mean and variance when the loss function is squared error plus linear cost. When we estimate them by using the smallest sample size such that the risk is minimized, the asymptotic optimal sample size contains the unknown parameter. Therefore we propose a sequential estimator and obtain the asymptotic expansions of the expected sample size and the risk of the sequential estimator as the cost per unit sample approaches zero.(2)We consider the point estimation problem of the powers of scale parameter of a normal distribution. We want to estimate the powers by using the smallest sample size such that the risk is less than or equal to a preassigned error bound when the risk is mean squared error. In this case the asymptotic optimal sample size contains the unknown parameter. Therefore we define a stopping rule and show that the risk is less than or equal to the error bound. Also, we consider the problem of estimating a scale parameter of an exponential distribution when the loss function is squared error plus linear cost.(3)We consider the bounded risk point estimation problem of the powers of scale parameter of an exponential distribution. We want to estimate the powers by using the smallest sample size such that the risk is less than or equal to a preassigned error bound when the risk is mean squared error. This smallest sample size cannot be used in practice, because it contains the unknown parameter. Therefore we propose a stopping rule and show that the condition of the risk is satisfied for sufficiently small error bound.

主要研究者和每位研究者直接或间接获得了与本项目标题相关的研究结果。主要研究者的主要结果如下。(1)We考虑损失函数为平方误差加线性成本时，均值和方差均未知的正态分布的标准差的幂的点估计问题。当我们用最小样本量估计它们时，使得风险最小化，渐近最优样本量包含未知参数。因此，我们提出了一个序贯估计，并获得了期望样本容量和序贯估计的风险的渐近展开的单位样本成本接近零。(2)We考虑正态分布尺度参数幂的点估计问题。我们希望通过使用最小样本量来估计功效，使得当风险为均方误差时，风险小于或等于预先指定的误差界。在这种情况下，渐近最优样本量包含未知参数。因此，我们定义了一个停止规则，并证明了风险小于或等于误差界。此外，我们考虑的问题，估计指数分布的尺度参数时，损失函数的平方误差加上线性成本。(3)We考虑指数分布尺度参数的幂的有界风险点估计问题。我们希望通过使用最小样本量来估计功效，使得当风险为均方误差时，风险小于或等于预先指定的误差界。这个最小样本量在实践中不能使用，因为它包含未知参数。因此，我们提出了一个停止规则，并证明了风险的条件是满足足够小的误差界。