High-Dimensional Statistical Inference for Multivariate Models and Its Applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330038
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Hiroshima University
• Principal Investigator: Fujikoshi Yasunori 広島大学, 理学(系)研究科(研究院), 名誉教授 (40033849)
• Co-Investigator(Kenkyū-buntansha): YANAGIHARA HIROKAZU 広島大学, 大学院理学研究科, 准教授 (70342615)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 多変量線形モデル / 多変量回帰モデル / 判別分析モデル / 成長曲線モデル / 変数選択法 / モデル選択規準 / 高次元性一致性 / 冗長性検定

Outline of Final Research Achievements

In this project we derived high-dimensional consistency properties for variable selection methods based on model selection criteria in multivariate linear model including multivariate regression model and discriminant analysis and in growth curve model. The model selection criteria treated includes AIC criterion, BIC criterion and Cp criterion. The high-dimensional properties were derived under a high-dimensional asymptotic framework such that the ratio of the number of response variables to the sample size tends to a fixed number less than 1. Further, we derive a high-dimensional asymptotic distribution for the likelihood ratio criterion for testing an additional information hypothesis in canonical correlation analysis and its error bound.

Free Research Field

統計科学