Research on new developments of theory of statistical inference in several modern problems in multivariate analysis

2017 Fiscal Year Final Research Report

• Project/Area Number: 26330036
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: The University of Tokyo
• Principal Investigator: Kubokawa Tatsuya 東京大学, 大学院経済学研究科(経済学部), 教授 (20195499)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 線形混合モデル / 小地域推定 / 高次元解析 / 統計的決定理論 / 共分散行列 / 縮小推定 / 経験ベイズ / 階層ベイズ

Outline of Final Research Achievements

In this research project, I addressed several problems in multivariate data analysis, derived new statistical methods to solve the problems and developed theory on their usefulness and optimality. The performances of the suggested methods were investigated through simulation experiments and data analysis. In particular, I obtained research results for the following five topics: (A) New developments in small area estimation based on linear mixed models and generalized linear mixed models, (B) Benchmark problems in small area estimation, (C) Variable selection in linear mixed models, (D) Use of shrinkage estimation methods in high-dimensional multivariate analysis, and (E)Developments of optimality theory in multivariate statistical inference.

Free Research Field

数理統計学