2013 Fiscal Year Final Research Report
New developments of theories in multivariate statistical inference and their applications
| Project/Area Number |
21540114
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KUBOKAWA Tatsuya 東京大学, 経済学研究科(研究院), 教授 (20195499)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 多変量解析 / 線形混合モデル / 小地域推定 / 統計的決定論 / バートレット補正 / 高次元解析 / 漸近不偏性 / ベイズ推測 |
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| Research Abstract |
In this research project, new procedures were derived in estimation, hypothesis testing, predction and variable selection in multivariate statistical models as well as theories for justfying the new procedures were developed. In particular, we treated problems, models or situations where conventional methods had drawbacks for use or were not available, and then we tried to derive and suggest procedures which could resolve the problems. Of these, the following multivatiate statistical issues were addressed and new theories were developed with applications: (1) higher order asymptotic corrections in mean squared errors and confidence intervals in small area estimation, (2) benchmark problems in small area estimation under continuous and discrete mixed models, (3) Bartlett corrections and methods for variable selection in linear mixed models, (4) high dimensional procedures in linear discrimination and (5) optimality in estimation of multi-dimensional parameters.
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