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.

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)当损失函数为平方误差加线性成本时，我们考虑均值和方差未知的正态分布的标准差幂的点估计问题。当我们使用最小样本量来估计它们以使风险最小化时，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器，并获得了期望样本量的渐近展开以及当单位样本成本接近零时序贯估计器的风险。(2)我们考虑了正态尺度参数幂的点估计问题分配。我们希望通过使用最小样本量来估计功效，以便当风险为均方误差时，风险小于或等于预先分配的误差界限。在这种情况下，渐近最优样本量包含未知参数。因此，我们定义一个停止规则并表明风险小于或等于错误界限。此外，我们还考虑了损失函数为平方误差加上线性成本时指数分布尺度参数的估计问题。(3)考虑了指数分布尺度参数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，以便当风险为均方误差时，风险小于或等于预先分配的误差界限。这个最小的样本量不能在实践中使用，因为它包含未知的参数。因此，我们提出了一个停止规则，并表明对于足够小的误差范围满足风险条件。