非齐次等式约束下奇异型线性回归模型的广义条件岭估计  

Generalized Conditional Ridge Estimation in Constrained Singular Linear Regression Model of Nonhomogeneous Equations

作　　者：朱宁[1] 赵肖肖[1] 李绍波[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《汕头大学学报（自然科学版）》2012年第2期54-62,共9页Journal of Shantou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(71001015)

摘　　要：文章对线性回归模型参数有偏估计做进一步研究,提出了在非齐次等式约束下奇异型线性回归模型参数的广义条件岭估计,并给出它的一些性质,而且证明了在一定条件下,在均方误差阵和广义均方误差意义下,广义条件岭估计都优于约束最小二乘估计.最后,通过实际数据进行实证分析,得到了取不同岭参数矩阵时对应的广义条件岭估计及其MSE,验证了广义条件岭估计优于约束最小二乘估计的充分条件的正确性.The linear regression model parameter biased estimation is further researched. The generalized conditional ridge estimation is studied in constrained singular linear model of nonhomogeneous equations and some of its properties are given. It is proved that in certain conditions, general conditions of ridge estimators are better than the constrained least squares estimator in the mean square error matrix and generalized mean square error sense. Finally, by conducting empirical analysis of the actual data, the corresponding generalized conditional ridge type estimation and its MSE are obtained when different ridge parameters are chosen. The sufficient condition that the generalized conditional ridge estimation excels the restricted least squares estimator is verified.

关 键 词：最小二乘估计 约束最小二乘估计 广义条件岭估计 广义均方误差 均方误差阵 

分 类 号：O212.4[理学—概率论与数理统计]