Basic research on resampling of the bootstrap type

2014 Fiscal Year Final Research Report

• Project/Area Number: 24500350
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Tokyo University of Science
• Principal Investigator: NIKI Naoto 東京理科大学, 工学部, 教授 (10000209)
• Co-Investigator(Renkei-kenkyūsha): ONO Yoko 横浜市立大学, 総合科学部, 准教授 (60339140) ; HASHIGUCHI Hiroki 東京理科大学, 理学部, 准教授 (50266920) ; NAKAGAWA Shigekazu 倉敷芸術科学大学, 産業科学技術学部, 教授 (90248203)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: コンピュータ支援統計 / 数式処理 / 統計量分布 / 対称式 / 統計的汎関数

Outline of Final Research Achievements

Resampling methods are designed in order to obtain approximated distributions of statistics by means of repeated sampling from the empirical distribution based on a sample from a population. Despite the frequent use to small size samples, only their asymptotic aspects for infinity in size have been discussed, excluding the reports on numerical experiments.
The main target of this research is to represent the characteristics of the resampled empirical distributions exactly, from the perspective that resampling is to sample a weight vector given to observation vector. The moments that characterize the distribution of the moments of the resampled distribution (moments-of-moments) have been written in terms of the moments of the original sample and the weight distribution; the moments-of-moments-of-moments are also obtained in terms of the population moments and the weight moments. The results seem useful for comparison between existing methods and for generation of new ideas.

Free Research Field

統計科学