Computing confidence levels of many hypotheses for high-dimensional data

2015 Fiscal Year Final Research Report

• Project/Area Number: 24300106
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Osaka University
• Principal Investigator: Shimodaira Hidetoshi 大阪大学, 基礎工学研究科, 教授 (00290867)
• Co-Investigator(Kenkyū-buntansha): SHIMIZU Shohei 大阪大学, 産業科学研究所, 准教授 (10509871) ; KANAMORI Takafumi 名古屋大学, 大学院情報科学研究科, 准教授 (60334546)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: ブートストラップ / リサンプリング / スケーリング則 / 仮説検定 / モデル選択 / 情報幾何 / 高次漸近理論 / 多変量解析

Outline of Final Research Achievements

Bootstrap method has a large approximation error for computing a confidence level by resampling from data. For computing confidence levels with higher accuracy, multiscale bootstrap method utilizes a scaling-law of probability when changing the sample size of data, and double bootstrap method adjusts the approximation error by resampling. In this research, multiscale double bootstrap method has been proposed by using these two existing approaches together. We proved that the new method further improves the accuracy. In terms of the geometry of the space of probability distributions, the approximation error of bootstrap is expressed as a “mean curvature” of the boundary surface of hypothesis, and that of double bootstrap is expressed as a “mean curvature of the mean curvature”, and they are removed by multiscale bootstrap.

Free Research Field

統計科学