Theoretical Research of Sequential Analysis and its Applications
Project/Area Number 
10640126

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Kumamoto University 
Principal Investigator 
TAKADA Yoshikazu Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (70114098)

CoInvestigator(Kenkyūbuntansha) 
YOKOYAMA Takahisa Tokyo Gakugei University, Faculty of Education, Associate Professor, 教育学部, 助教授 (20240864)
SAKATA Toshio Kumamoto University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (20117352)
山元 淳 熊本大学, 理学部, 講師 (50040100)
岡 幸正 熊本大学, 理学部, 助教授 (50089140)
大脇 信一 熊本大学, 理学部, 教授 (50040506)
櫃田 倍之 熊本大学, 理学部, 教授 (50024237)

Project Period (FY) 
1998 – 1999

Project Status 
Completed (Fiscal Year 1999)

Budget Amount *help 
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)

Keywords  Sequential estimation / Twostage procedure / Confidence region / Bounded risk problem / Simultaneous confidence interval / Asymptotic efficiency / 漸近有効 / 逐次解析 / 二標本問題 / 多変量正規分布 / 二段階推定法 / 非対称損失関数 
Research Abstract 
1. We got a condition which implies the nonexistence of parametric statistical procedures with bounded risk. Many examples for which such a condition is satisfied are considered. 2. Under an asymmetric loss function we considered if there exists a fixedsample procedure with bounded risk for a locationscale family. If there does not exist such a procedure, we constructed a procedure by employing a twostage procedure. 3. We consider the problem of constructing a fixedsize confidence region for a linear function of mean vectors of κmultinormal populations, where all covariance matrices are completely unknown. A twostage procedure is proposed to construct such a confidence region. It is shown that the proposed twostage procedure is consistent and its asymptotic property for the expected sample size is also given. A Monte Carlo simulation study is given for an illustration. 4. The problem of constructing an estimator with al risk bounded by a preassigned number is considered for a linear function of mean vectors of κmultinormal distributions when covariance matrices are fully unknown. We provide a new twostage procedure which does improve the previous one. The procedure is shown to be asymptotically efficient. 5. The problem of constructing a set of fixedwidth simultaneous confidence intervals for the treatmentcontrol differences of means is considered for several independent normal populations with a common unknown variance. A twostage procedure is developed for such inference and its asymptotic characteristics are studied up to the second order. Finally; performances of the proposed twostage procedure are compared for both small and moderate sample sizes in several cases.

Report
(3 results)
Research Products
(13 results)