Theoretical development of bootstrap and empirical likelihood method for method of spatio-temporal data
| Project/Area Number |
17K12652
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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 | Waseda University (2019-2020)
Kyoto University (2017-2018) |
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Principal Investigator |
Liu Yan 早稲田大学, 理工学術院, 研究院講師 (10754856)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Discontinued (Fiscal Year 2020)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 時系列解析 / 経験尤度法 / 予測・補間 / 漸近理論 / 高次元統計解析 / 漸近有効性 / 頑健性 / 分位点解析 / 統計科学 / 高次元 / 経験尤度 / 局所定常 / ハーディ空間 / 統計的検定論 / 分位点 / ブートストラップ / 欠損値解析 / 統計的漸近理論 / 頑健的統計手法 / 分位点法 / 判別分析 / ポートフォリオ理論 / 統計学 / 解析・評価 / 時空間データ / ブートストラップ法 |
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| Outline of Final Research Achievements |
In time series analysis, statistical inference has been developed under regular conditions. It is well known that financial data do not have finite variance. In other words, the data do not satisfy the regular conditions. We applied the empirical likelihood method with the self-standardized periodogram to stable processes, known as stochastic processes with infinite variance. We also derived the asymptotic distributions and proposed a method for constructing the confidence region for pivotal quantities. As a wide class of time-series models including stable processes, we considered the prediction or interpolation error as a divergence between the true model and the parametric model, and developed the theoretical statistical inference for this method. In particular, the characteristics of the proposed statistical method were mathematically discussed from various viewpoints such as asymptotic effectiveness and robustness. These achievements have been summarized in a book and papers.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、正則条件を満たさない時系列データを想定した時系列解析を理論的に研究した。学術的には、正規過程に対する統計解析が多かったが、本研究では、それを含めた安定過程のクラスでの統計解析を研究し、これまでとは異なる漸近論を展開することに成功した。通常、感染性疾病の伝染経路、世界中の取引所の金融データは正規過程に従わないため、本成果は汎用的な統計解析を実現した。経験尤度法の開発は社会的にも、広い範囲における観測データを、より正確で迅速的な統計解析の実現に繋がっており、情報の蓄積やその利用に直結しているため、統計学の観点による最善策に基づき、利益の向上や、リスクを最小限に食い止めることに繋がる。
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Report
(4 results)
Research Products
(37 results)
