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带有结构变化的线性模型中参数估计的一些结果 被引量：4

SOME RESULTS ON PARAMETER ESTIMATION IN A LINEAR MODEL WITH STRUCTURAL CHANGE
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摘要 本文在一些纯量损失和矩阵损失下研究带有结构变化的正态线性模型中参数的估计问题．分别给出 了存在回归系数的一致最小风险无偏（ＵＭＲＵ）估计和一致最小风险同变（ＵＭＲＥ）估计的充要条件， 证明了不存在误差方差在仿射变换群下的ＵＭＲＥ估计．导出了回归系数的最小二乘估计的可容许性 和极小极大性． The problem of estimating parameters in a normal linear model with structural change under some scalar losses and matrix losses is studied. The necessary and sufficient exis- tence conditions aret respectively given for the uniformly minimum risk unbiased (UMRU) estimator and the uniformly minimum risk equivariant (UMRE) estimator of regression coef- ficients. It is proved that no UMRE estimators of error variances under an whne group exist. The admissibility and minimaxity of the least squares estimator of regression coefficients are also derived.
作者 吴启光 徐兴忠
机构地区 中国科学院系统科学研究所
出处 《数学年刊（A辑）》 CSCD 北大核心 2001年第5期607-616,共10页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.19871088)
关键词 可容许估计 极小极大估计 一致最小风险无偏估计 线性模型 参数估计 UMRU估计 回归 正态误差 Admissible estimator, Minimax estimator, Normal linear model with structural change, Uniformly minimum risk equivariant estimator,
分类号 F224.7 [经济管理—国民经济]
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参考文献11

  • 1[1]Anndrew, D. W. K. & Fair, R. C., Inference in econometric models with structural change [J], Review of Economic Studies, 55(1988), 615-639.
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同被引文献30

  • 1吴启光.Necessary and Sufficient Conditions for the Existence of UMRU Estimators in Growth Curve Model[J].Chinese Science Bulletin,1994,39(2):89-92. 被引量：1
  • 2韦博成.加权非线性回归的Score检验及其局部影响分析[J].应用概率统计,1995,11(2):147-156. 被引量：23
  • 3JIRO H. Finite-sample properties of single-equation estimators under-structural change[J]. Journal of Econometrics,1992,53(1-3):189-209.
  • 4DONALD W K,ANDREWS R C F. Inference in nonlinear econometrics models with structural change[J].The Review of Economic Studies,1988,55(4):615-639.
  • 5COOK R D. Assessment of local influence[J]. J R Statist Soc,1986,B-48:133-169.
  • 6RATKOWSKYDA 洪再吉 韦博成 吴诚鸥 译.非线性回归模型--统一的实用方法[M].南京:南京大学出版社,1986.49-59.
  • 7Kubokawa T. Double shrinkage estimation of common coefficients in two regression equations with heteroscedasticity [ J ].Journal of Multivariate Analysis, 1998, 67:169 - 189.
  • 8Cook R D. Assessment of local influence [ J ]. J R Statist Soc B, 1986, 48 (2): 133 - 169.
  • 9Wei B C. Exponential family nonlinear models [M]. Singapore: Springer-Verlag, 1998. 123 - 135.
  • 10Thomas W. Influence on confidence regions for regression coefficients in generalized linear models [ J ]. JASA, 1990, 85(410) :393 - 397.

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数学年刊（A辑）
2001年 第5期

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