On asymptotic higher-order properties of sequential sampling methods

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540107
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Akita University
• Principal Investigator: UNO Chikara 秋田大学, 教育文化学部, 教授 (20282155)
• Co-Investigator(Kenkyū-buntansha): YAMAGUCHI Yoshikazu 秋田大学, 教育文化学部, 准教授 (30534044)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 逐次解析 / 二段階法 / 漸近有効性 / 停止時間

Outline of Final Research Achievements

There are some statistical estimation problems for which no procedures of fixed sample size are available. For these problems, we can solve them by means of sequential sampling methods where the sizes of sample are random variables. In this research, we investigated asymptotic properties of two-stage procedures in which the samples are taken twice. When the lower bound for the variance is known, we inserted the known lower bound into the two-stage procedure and researched its asymptotic efficiency. For the problem of constructing fixed-width confidence interval, we established higher-order asymptotic theory on the rate of convergence of the coverage probability to the confidence level 1 minus alpha as the width tends to zero.

Free Research Field

統計数学