Mean Pythagorean Relations in the Estimation of the Multi-dimensional Parameter

多维参数估计中的平均毕达哥拉斯关系

• 批准号: 06680297
• 负责人: YANAGIMOTO Takemi
• 金额: $ 0.96万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06680297/
• 关键词: Pythagorean relation; Evaluation of an estimator; Nonparametric regression method; GLM; Parameter orthogonality; 最尤推定量; 条件付最尤推定量; 推定関数; 経験Bayes法; 推定量の良さ

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.

Kullback-Leibler损失现在甚至在信息论和量子力学中也很重要。本研究的目的是通过我们对概率分布空间结构的更深入理解来发展新的方法。目标领域是：1）条件似然法和边际似然法，2）经验贝叶斯法，3）估计方程法，本课题的主要研究成果如下：1）利用对偶概念探讨了参数的正交性。这项研究使我们对GLM的基础有了更深的理解，也为我们提供了关于LRT的新发现。2）参数回归方法与非参数回归方法之间存在着严重的差距。然而，人们相信，各种共同的属性仍然存在。这一猜想是利用肯定通过模拟研究。因此，下一步将是探索发现的理论背景。3）MLE的一个实质性缺陷是其潜在的过拟合。在与伊原教授（大坂经济大学）进行的因素分析中对此进行了研究。基础研究涉及到渐近二阶结构的MLE通过Kullback-Leibler损失和正交参数坐标。尽管这些问题很重要，但对它们的研究却很少。江口教授（ISM）和山本教授（冈山美国）积极参与这些联合研究。

项目成果

T. Yanagimoto: "The mean Pythagorean relation in the nonparametric regression method" J. Statist. Research. 28. 177-187 (1994)

T. Yanagimoto：“非参数回归方法中的平均毕达哥拉斯关系”J. Statist。

Yamamoto,E & Yanagimoto,T.: "A modified likelihood ratic test for the mean direction in the von Mises distribution" Covmmunication In Statistics-Theny and Method. 24. 2659-2678 (1995)

山本E

T. Yanagimoto: "The Kullback-Leibler risk of the Stein estimator and the conditional MLE" Ann. Inst. Statist. Math.46. 29-41 (1994)

T. Yanagimoto：“Stein 估计量和条件 MLE 的 Kullback-Leibler 风险”Ann。

柳本武美: "推定方程式に基づく推定" 応用統計学. 24. 1-12 (1996)

Takemi Yanagimoto：“基于估计方程的估计”应用统计学 24. 1-12 (1996)。

T.Yanagimoto: "Discrete first passage time distribution for describinginequality among individuals." In Lifetime Data : Models in Reliability and Survival Analysis (eds.N.P.Jewel et al.), Kluwer Academic. 377-383 (1996)

T.Yanagimoto：“离散首次通过时间分布用于描述个体之间的不平等。”