| Project/Area Number |
12680314
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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 |
Statistical science
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| Research Institution | GIFU UNIVERSITY |
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Principal Investigator |
SAGAE Masahiko GIFU University, Faculty of Engineering, ASSOCIATE PROFESSOR, 工学部, 助教授 (20215669)
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| Co-Investigator(Kenkyū-buntansha) |
KOGURE Atsuyuki KEIO University, Faculty of Policy Management PROFESSOR, 総合政策学部, 教授 (80178251)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2002: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | method of local moments / maximum entropy principle / density estimation / ノンパラメトリック / 確率密度関数 / ヒストグラム / 局所モーメント法 / ノンパラメントリック法 / 最大エントロピー原理 |
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| Research Abstract |
A local log polynomial density estimator is proposed based on the maximum entropy principle and is also done as a well-defined model in order to remove the problem of negativity that can occur in certain region of the polynomial histogram by Sagae and Scott (1997). Our estimating approach based on the method of local moments might be viewed as a method matching the corresponding local model to the localized sample moments. We call this density function the "Maximum Entropy Density (MED)". The MED is a "bona fide" density function, that is, nonnegative everywhere with integral to one. We show that the MED can achive the higher order convergence rates parallel to the results for the polynomial histogram.
We also discuss a close relation and the difference between the method of local moments and the local likelihood method for the log-polynomial density function. Our method can be seen as a way for estimating the continuous density function from the aggregated data and may provide a wide range of applications in fields such as economics where it is often the case that the first data available are pre-binned or rounded prior for the data analysis.
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