线性回归模型中K-d型估计研究 |
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引用本文: | 何剑,吴平,胡欣.线性回归模型中K-d型估计研究[J].新乡学院学报(自然科学版),2010,27(6):14-15,26. |
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作者姓名: | 何剑 吴平 胡欣 |
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作者单位: | 空军雷达学院,基础部,湖北,武汉,430019 |
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摘 要: | 考虑线性回归模型Y=Xβ+ε,E(ε)=0,Cov(ε)=σ2 I,当设计矩阵X的列存在共线性时,最小二乘估计β=(X′X)-1 X′Y的性质变坏,为此给出了有偏估计β(K,d)=(X′X+K)-1(X′Y+dβ),其中K〉0为对角矩阵,ki〉0,-∞〈d〈∞为参数,讨论了这种有偏估计对Liu估计、最小二乘估计的优越性,并证明了其可容许性估计。
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关 键 词: | 有偏估计 Liu估计 最小二乘估计 可容许性估计 |
New Research of Liu Estimation on Linear Regression Model |
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Authors: | HE Jian WU Ping HU Xin |
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Institution: | (Department of the Basic Courses,AFRA,Wuhan 430019,China) |
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Abstract: | Considering the linear regression model Y = Xβ + ε,E(ε) = 0,Cov(ε)= σ 2 I,when the design matrix X in the presence of linear time,the nature of perishable least squares estimationβ=(X ′X) -1 X ′Y is bad,a biased estimate β(K,d)=(X ′X + K) -1(X ′Y +d β) was presented,among which K is diagonal matrix,ki 0,-∞ d ∞ are parameters,and the difference of this biased estimates between Liu estimated and least squares estimation is discussed. |
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Keywords: | biased estimate Liu estimation least squares estimation admissible estimation |
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