带线性约束的回归模型参数的Liu估计方法

LIU-TYPE ESTIMATION FOR THE LINEAR MODEL WITH LINEAR RESTRICTIONS

针对一般带约束的最小二乘估计(ORLSE)在参数估计中处理复共线性的不足,通过引入附加随机线性约束,提出了约束Liu型估计方法。经理论证明,此方法在均方误差下较已经提出的ORLSE和约束岭估计(RRE)效果更好,并且它可以作为两种方法的推广形式。讨论了其中k,d的确定原则,并将此方法推广到了广义形式和典则形式下的估计公式。

For the multicollinearity in restricted linear regression, there are some problems still left open in current popular ordinary restricted least square estimation. By introducing stochastic linear restrictions, a restricted Liu-type estimation is proposed, which generalizes the ordinary restricted least square estimation and restricted ridge estimation. Then the selection method of the scalars k and d is disscussed and is generalized to the estimation of restricted linear model and canonical form.