1995 Fiscal Year Final Research Report Summary
Mean Pythagorean Relations in the Estimation of the Multi-dimensional Parameter
| Project/Area Number |
06680297
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
YANAGIMOTO Takemi The Institute of Statistical Mathematics, Department of Interdisciplinary Statistics, Professor, 領域統計研究系, 教授 (40000195)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Pythagorean relation / Evaluation of an estimator / Nonparametric regression method / GLM / Parameter orthogonality |
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| Research Abstract |
The Kullback-Leibler loss is now important even in information theory and quantum mechanics. The aim of the present research is to develop new methods through our deeper understanding of the structure of the apace of probability distributions. The targeted areas are : 1) The conditional likelihood method and the marginal likelihood method, 2) The empirical Bays method, and 3) The estimating equation method.
The finding obtained as the present research project are summerized as follow :
1) Parameter orthogonality is explored through the notion of duality. This study brings us to deeper understanding of the foundation of GLM.It provides us also with a new finding of the LRT.Recent discussions with Dr.Kawanabe (Tokyo U.) suggest a close relation between parameter orthogonality and the theory of estimating functions.
2) There is a severe gap between the paramentric and the nonparamentric regression methods. However, it is believed that various common properties still hold. This conjecture is exploited affirmatively through simulation studies. Thus the next step will be to explore theoretical backgrounds of the findings.
3) A substantial defect of the MLE is expected as its potential overfitting. This is examined in the factor analysis, which was conducted with Prof.Ihara (Osaka E.I.U.).
Foundamental researches pertain to the asymptotic second order structure of the MLE through the Kullback-Leibler loss and also to orthognal parameter coordinats. Researches on these subjects look sparse in spite of their importance. Professors Eguchi (ISM) and Yamamoto (Okayama U.S.) participated agressively to these joint researches.
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