| Project/Area Number |
17K00041
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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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| Research Field |
Statistical science
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| Research Institution | Hokkaido University |
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Principal Investigator |
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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 |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ノンパラメトリック法 / 密度推定 / 境界バイアス / ノンパラメトリック / ノンパラメトリック密度推定 |
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| Outline of Final Research Achievements |
We mainly study the asymmetric kernel methods to estimate the probability density for nonnegative data. Especially, we have aimed at developing unified asymmetric kernels (rather than the kernel specific analysis); thus, to create asymmetric kernel density estimators in a flexible way, we have proposed (i) a family of Amoroso kernels, including gamma/inverse gamma kernels as special cases and (ii) a family of symmetrical-based q-MIG kernels or a family of skew-based non-central q-BS kernels. Also, we have discussed (iii) (higher-order) bias-corrected asymmetric kernel density estimators, (iv) multivariate non-central BS kernel density estimators, and so on. We have derived asymptotic formulas of bias, variance, and mean (integrated) squared error of the proposed estimator, together with strong consistency and asymptotic normality. We further have conducted the simulation studies to confirm our theoretical results.
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| Academic Significance and Societal Importance of the Research Achievements |
非負データのノンパラメトリック推測に応用可能な非対称カーネルが、個別的ではなく、統一的に構築された。特に、対称分布ベースのｑ－ＭＩＧカーネル族、及び、歪分布ベースの非心ｑ－ＢＳカーネル族は、密度生成機と呼ばれる無限次元の関数の自由度を持ち、多義的に拡張が可能であり、極めて柔軟な非対称カーネル族を形成できている特徴がある。これらは単変量の非負データに関する密度推定に留まらず、多変量非負データの密度、２標本問題における密度比、条件付き密度、ハザード比などのノンパラメトリック関数推定へ応用できる見込みがあり、今後、この方面からの進展が期待される。
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