齐次等式约束线性回归模型回归系数的综合条件岭估计  

The Synthesized Conditional Ridge Estimation of Regression Coefficient in the Homogeneous Equation Restricted Linear Regression Model

作　　者：农秀丽[1] 

机构地区：[1]广西民族师范学院数学与计算机科学系,中国崇左532200

出　　处：《湖南师范大学自然科学学报》2012年第2期7-13,共7页Journal of Natural Science of Hunan Normal University

基　　金：广西自然科学基金资助项目(2010GXNSFA013116);广西高校优秀人才基金资助项目(桂教人〔2010〕65号);广西民族师范学院基金资助项目(ybxm200908)

摘　　要：提出了齐次等式约束线性回归模型回归系数的一个新的有偏估计,即综合条件岭估计.讨论了综合条件岭估计的可容许性等优良性质.给出了其迭代解和极小化均方误差的无偏估计解.在一定的条件下,综合条件岭估计的样本总方差、均方误差、均方误差矩阵均分别小于约束最小二乘估计的相应误差.条件岭估计和条件根方估计为综合条件岭估计的特例,从而统一了条件岭估计和条件根方估计的理论.A new biased estimation of regression coefficient in a regression model with homogeneous equality constraints, the synthesized conditional ridge estimation, is proposed. Some properties of the new biased estimation, such as admissibility, are proved. The iterative solution and the unbiased estimation solutions minimizing the mean square error are given. Under some conditions, covariance, mean square error and mean square error matrix of the synthesized conditional ridge estimation are less than that of constrained least squares estimation. Two methods for evaluating this estimation are introduced. Synthesized conditional estimation includes the conditional ridge estimation and root estimation as special eases, which unified the theories on conditional ridge estimation and root estimation.

关 键 词：回归模型 条件岭估计 条件根方估计 均方误差 均方误差矩阵 

分 类 号：O212.4[理学—概率论与数理统计]