A sequential analytic approach to the methods of optiaml statistical decisions

最优统计决策方法的序贯分析方法

• 批准号: 09640251
• 负责人: ISOGAI Eiichi
• 金额: $ 1.66万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640251/
• 关键词: probabilty density estimation; sequential estimation; stopping rule; asymptotic efficiency; confidence interval; biased-corrected; normal distribution; exponential distribution; 確率密度推定; 正規分府; パーセント点; 漸近的一致性; 2次漸近有効

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) For the problem of estimating nonparametric probability density function with preassigned bound of mean integrated squared error we proposed sequential density estimators, and showed their asymptotic efficiency.(2) We considered sequential fixed-width confidence interval estimation for a linear combination of mean and standard deviation of a normal distribution with mean and variance both unknown. We constructed sequential confidence intervals with preassigned fixed-width and coverage probability, and their asymptotic consistency.(3) We considered the sequential point estimation of the nonzero mean under squared relative error plus linear cost as a loss function. We proposed a sequential procedure and showed this procedure has a risk less than that of the existing procedure for a certain clas of distributions.(4) We considered the problem of bounded risk point estimation for the scale parameter of a nagative exponential distribution under a certain loss function. We proposed two sequential estimators, and gave the asymptotic expansions of the risk associated with them.

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）对于估计具有预先指定的均方积分误差界限的非参数概率密度函数的问题，我们提出了序贯密度估计器，并展示了它们的渐近效率。（2）我们考虑了序贯固定-均值和方差均未知的正态分布的均值和标准差的线性组合的宽度置信区间估计。我们构建了具有预先指定的固定宽度和覆盖概率的顺序置信区间及其渐近一致性。（3）我们将平方相对误差加上线性成本下的非零均值的顺序点估计视为损失函数。我们提出了一个序贯过程，并表明对于某一类分布，该过程的风险小于现有过程的风险。(4)我们考虑了在一定条件下负指数分布的尺度参数的有界风险点估计问题。损失函数。我们提出了两个序贯估计量，并给出了与它们相关的风险的渐近展开式。

项目成果

Masafumi Akahira: "The existence of a test with the largest order of consistemcy in the case of a a two-sided Gamma type distribution" Metron. 55・1-2. 93-107 (1997)

Masafumi Akahira：“在双面 Gamma 型分布的情况下存在最大阶一致性检验”Metron 55・1-2 (1997)。

Keiji Izuchi: "BKW-operators on the interval [0,1]" Rendiconti de circolo Matematico di Palermo(2). 46・3. 477-489 (1997)

Keiji Izuchi：“区间 [0,1] 上的 BKW 算子”Rendiconti de circolo Matematico di Palermo(2) 477-489 (1997)。

Keiji Izuchi: "BKW-operators on the interval[0,1]" Rendiconti del Circolo Matematico di Palermo(2). 46・3. 477-489 (1997)

Keiji Izuchi：“区间 [0,1] 上的 BKW 算子”Rendiconti del Circolo Matematico di Palermo(2) 477-489 (1997)。

Yutaka Kimura: "On duality of discrte time stochastic control processes" Bulletin of Informatics and Cyberreties. 29・1. 91-103 (1997)

Yutaka Kimura：“关于离散时间随机控制过程的对偶性”，信息学和网络科学通报 29・1（1997）。

Shigeo Akashi: "Superposition representability problems of quantum information chanaels" Open Systems and Information Dynamics. 4・1. 45-52 (1997)

Shigeo Akashi：“量子信息通道的叠加表示性问题”开放系统和信息动力学4·1（1997）。