Separate inference induced from the structure of a statistical model

从统计模型的结构中导出的单独推论

• 批准号: 08680340
• 负责人: YANAGIMOTO Takemi
• 金额: $ 1.09万
• 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 Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680340/
• 关键词: Conditional MLE; GEE; Marginal Likelihood; Empirical Bays method; MLE; 直交性; 推定関数の不変性; 多次元母数; スタイン推定量; 対数線型モデル

1) It becomes clear that a useful model in practical applications involves in more parameters (parameters of high-demensions) than it is previously believed. A low-dimensional parameter is unble to describe a practical situation. Here we should note that the crude MLE behaves unfavorably in estimating a high-dimensional parameter. My previous efforts went to modifying the MLE through the conditional MLE,the estimating equation.2) The present research aimed at introducing a new family of distributions named the ruled exponential distributions. Then analytical properties of the family and their applications were discussed. A simple estimating function is investigated in relation with a family of distributions.3) More explicitly, the MLE based on a separate likelihood, mainly in the ruled exponential family, was pursued. Further, the present research extended to an obvious application to the estimating function and also to a modification of the family.4) A challenging topic is to unify the generalized regression model and the Stein type estimator. The present approach looks promising. We are making efforts to contributing this important problem, though a bulk of difficulties arise.

1)很明显，在实际应用中，一个有用的模型所涉及的参数（高维参数）比以前认为的要多。低维参数无法描述实际情况。这里我们应该注意到，粗糙的MLE在估计高维参数时表现不佳。我之前的努力是通过条件MLE，估计方程来修改MLE。2)本研究旨在引入一类新的分布，称为正则指数分布。然后讨论了该族的分析性质及其应用。研究了一类分布的简单估计函数。3)更明确地，主要在规则指数族中，追求基于单独似然的最大似然。进一步，本研究扩展到对估计函数的明显应用，也扩展到对族的修改。4)统一广义回归模型和Stein型估计量是一个具有挑战性的课题。目前的方法看起来很有希望。尽管出现了许多困难，但我们正在努力解决这一重要问题。

项目成果

Yanagimoto, T.and Hiejima, Y.: "Separate optimum estimating function for the ruled exponential family." Insititute of Mathematical Statistics Lecture Notes-Monograph Series.Selected Proceedings of the Symposum on Estimating Function. vol.32. 457-462 (1998

Yanagimoto, T. 和 Hiejima, Y.：“规则指数族的单独最佳估计函数。”

柳本 正勝、柳本 武美: "1人当たり穀物生産量減少の時代-FAO農業生産年報傾向分析結果による-" 世界の農林水産. 2月号. 26-32 (1998)

Masakatsu Yanagimoto、Takemi Yanagimoto：“人均粮食产量下降的时代——基于粮农组织农业生产年度报告的趋势分析结果——”世界农业、林业和渔业2月26-32日（1998年）。

Yanagimoto, M.and Yanagimoto, T.: "Production amount of cereals per capita is decreasing in latest years." World Agricultrue, Forestry and fisheries. 26-32 (1998)

Yanagimoto, M. 和 Yanagimoto, T.：“近年来人均谷物产量正在下降。”