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Studies on efficiency of statistical methods of sequential estimation

序贯估计统计方法的有效性研究

基本信息

批准号：
16540099
负责人：
ISOGAI Eiichi
金额：
$ 2.24万
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：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

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 considered the minimum risk sequential point estimation problem for a function of the scale parameter of an exponential distribution subject to the loss function given as a sum of the squared error and a linear cost. We want to estimate the function by using the sample size which minimizes the risk of the expectation of the loss. Then the smallest sample size contains the unknown parameter. Therefore, we proposed a fully sequential procedure and gave the second-order expansion of the expected sample size and risk when the cost per unit observation tended to zero.(2) We considered the problem of estimating a function of two scale parameters from two exponential populations. We want to construct a confidence interval of the function with given length and confidence coefficient. The asy … More mptotic smallest sample size contains the unknown parameters, so we proposed a fully sequential sampling procedure and sequential confidence intervals. We showed that these sequential confidence intervals have asymptotic consistency and gave the second-order asymptotic expansion of the expected sample size.(3) We considered sequential bounded risk point estimation of the ratio of scale parameters of two exponential distributions subject to the loss function given as the squared error. We wish to estimate the ratio under the condition that the risk of the expected loss is bounded by a preassigned positive constant. The smallest sample size which satisfies the condition includes the unknown parameters. Therefore, we proposed a fully sequential sampling scheme and provided second order approximation of the expected sample size and the risk of the sequential procedure. We also proposed a bias corrected sequential procedure to reduce the risk and obtained a second order approximation of its risk. Less

主要研究者和每个研究者获得的结果直接或间接与本项目的标题有关。首席研究员给出的主要结果如下。(1)考虑了指数分布尺度参数函数的最小风险序贯点估计问题，损失函数为误差平方和线性代价之和.我们希望通过使用样本大小来估计函数，该样本大小使损失期望的风险最小化。则最小样本量包含未知参数。因此，我们提出了一个完全序贯的过程，并给出了二阶扩展的期望样本容量和风险时，每单位观测成本趋于零。(2)考虑了从两个指数总体估计两个尺度参数的函数的问题。我们想要构造具有给定长度和置信系数的函数的置信区间。The Asy ...更多信息最小样本容量包含了未知参数，因此我们提出了一种完全序贯抽样方法和序贯置信区间。我们证明了这些序贯置信区间具有渐近相合性，并给出了期望样本容量的二阶渐近展开式。(3)考虑了损失函数为平方误差时两个指数分布尺度参数之比的序贯有界风险点估计。我们希望在预期损失的风险由一个预先指定的正常数限制的条件下估计该比率。满足条件的最小样本量包含未知参数。因此，我们提出了一个完全序贯抽样方案，并提供了预期样本量和序贯程序的风险的二阶近似。我们还提出了一个偏差校正序贯程序，以减少风险，并获得了其风险的二阶近似。少

项目成果

期刊论文数量（60）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Sequential interval estimation of a location parameter with the fixed width in the uniform distribution with an unknown scale parameter

未知尺度参数的均匀分布中固定宽度位置参数的顺序区间估计

DOI：
发表时间：
2005
期刊：
Sequential Analysis 24, 1
影响因子：
0
作者：
Yokura;S.;Masafumi Akahira and Ken-ichi Koike
通讯作者：
Masafumi Akahira and Ken-ichi Koike

Weighted loss functions for set estimation and testing hypotheses

用于集合估计和检验假设的加权损失函数

DOI：
发表时间：
2004
期刊：
Journal of the Japan Statistical Society 34・2
影响因子：
0
作者：
M.Akahira;K.Koike;Tadashi Takahashi;M.Akahira;Itsuro Kakiuchi;Masafumi Akahira;Shinnji Kuriki;Teruhiro Shirakura;Shogo Nishizawa;Tadashi Takahashi;Uno Chikara;Tadashi Takahashi;Nishizawa Shogo;稲葉太一;Itsuro Kakiuchi;Lim Daisy Lou;Shinji Kuriki;Maihara Hirosuke
通讯作者：
Maihara Hirosuke

Existence Theorem of Cone Saddle-Points Applying a Nonlinear Scalarization

应用非线性标量化的锥鞍点的存在定理