2022 Fiscal Year Final Research Report
Improvement of linear inequalities constrained parameters estimators
| Project/Area Number |
18K11196
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Mejiro University |
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Principal Investigator |
WATANABE Genso (張元宗) 目白大学, 社会学部, 客員研究員 (40227343)
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| Co-Investigator(Kenkyū-buntansha) |
篠崎 信雄 慶應義塾大学, 理工学部(矢上), 名誉教授 (70051886)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | shrinkage estimator / order statistics / multiplicative Poisson / predictive density / alpha-divergence / stochastic dominance / Pitman's closeness |
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| Outline of Final Research Achievements |
In estimating (p>=2) independent Poisson means, under the normalized squared error loss. We propose new classes of dominating estimators using prior information pertinently. Further, simultaneous estimation of Poisson means under order restriction is treated and estimators which dominate the isotonic regression estimator are proposed for some types of order restrictions. Shrinkage estimation of Poisson means is also considered when observations are given in the form of a two-way contingency table. Assuming a multiplicative Poisson model, estimators which shrink to the specified values or an order statistic in one dimension and in two dimensions are considered and are shown to dominate the MLE. Further, assuming the full model, shrinkage to the multiplicative model is devised to improve upon the unbiased estimator. Shrinkage is made after determining the basic cells so that the observed frequency is not smaller than the estimated frequency for each of the other cells.
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| Free Research Field |
数理統計、決定理論
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| Academic Significance and Societal Importance of the Research Achievements |
母数に制約条件、特に線形不等式制約条件がある場合の推定問題は数多く、古くから様々な研究がある。制約条件の下での最尤推定量（RMLE）が自然であるように思われるが、特に母数の数が多い場合には、正規分布の平均の推定問題でも、問題の次元、制約条件の数、推定する平均の線形関数に対して、未解明の部分が大きい。本研究では、まず正規分布の平均に線形不等式制約が存在する場合について状況を解明すること、ポアソン分布の場合でRMLE を改良すること、および、制約条件下での予測分布の推定量の改良問題を明らかにすることが数理統計決定理論上に意義がある。
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