Study on Statistical Methods based on Geometric and Algebraic Structures
| Project/Area Number |
17K12651
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Ogawa Mitsunori 東京大学, 大学院情報学環・学際情報学府, 特任講師 (50758290)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 統計数学 / ダイバージェンス / マルコフ基底 |
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| Outline of Final Research Achievements |
We developed a parameter estimation method for discrete exponential families under the presence of nuisance parameters. We used the framework of composite local Bregman divergences on discrete sample spaces and Markov bases from algebraic statistics. The resulting estimators are based on the conditional distributions given sufficient statistics for the nuisance parameters and do not require the calculations of the normalization constants of the conditional distributions. The consistency of the estimators is guaranteed by the connectivity of the underlying graph structures used in the construction of the divergences. We applied the proposed methods to the log-linear models of contingency tables and confirmed their usefulness.
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| Academic Significance and Societal Importance of the Research Achievements |
局外パラメータを含む統計モデルのパラメータ推定問題の歴史は長い．指数型分布族のように局外パラメータの十分統計量が存在する場合，十分統計量を所与とした条件付き分布に基づく推定量が統計的によい性質を持つことが知られている．しかし，条件付き分布の規格化定数は計算に適さない形であることが多く，実用上の障害になっていた．ダイバージェンスという幾何学的概念とマルコフ基底という代数統計由来の概念を組み合わせることにより，規格化定数の計算を経ないで興味あるパラメータを推定する方針が得られたことは，大きな意義も持つものである．
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Report
(4 results)
Research Products
(5 results)
