THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (S1): 103-109.

THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

陈建宝¹, 詹金龙²

1. Institute of Applied Mathematics, Yunnan Province, Kunming 650091, China;
2. Department of Basic Sciences, Kunming Institute of Technology, Kunming 650093, China

收稿日期:1992-11-05 出版日期:1994-12-31 发布日期:1994-12-31

THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

Chen Jianbao¹, Zhan Jinlong²

1. Institute of Applied Mathematics, Yunnan Province, Kunming 650091, China;
2. Department of Basic Sciences, Kunming Institute of Technology, Kunming 650093, China

Received:1992-11-05 Online:1994-12-31 Published:1994-12-31

摘要/Abstract

摘要： The present paper discusses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model:Y=X_e + e,E(e)=0, Cov(e)=σ²V, an new efficiency of least square estimate for linearly estimable function c' τ is proposed and its lower bound is given. For variance component model:Y=Xτ+ e, E(e)=0, Cov(e)=∑_i=1^mσ²V, an new efficiency of least square estimate for linearly estimable function c' τ is introduced for the first time and its lower bound, which is independent of unknown parameters, is also obtained.

关键词: Linear model, Gauss-Markov, Variance component, LSE, BLUE, Efficiency

Abstract: The present paper discusses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model:Y=X_e + e,E(e)=0, Cov(e)=σ²V, an new efficiency of least square estimate for linearly estimable function c' τ is proposed and its lower bound is given. For variance component model:Y=Xτ+ e, E(e)=0, Cov(e)=∑_i=1^mσ²V, an new efficiency of least square estimate for linearly estimable function c' τ is introduced for the first time and its lower bound, which is independent of unknown parameters, is also obtained.

Key words: Linear model, Gauss-Markov, Variance component, LSE, BLUE, Efficiency

陈建宝, 詹金龙. THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS[J]. 数学物理学报(英文版), 1994, 14(S1): 103-109.

Chen Jianbao, Zhan Jinlong. THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS[J]. Acta mathematica scientia,Series B, 1994, 14(S1): 103-109.

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THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

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