岭估计及其应用

最小二采估计是最小无偏估计。平差后,观测值的残差平方和为最小。在法方程系数矩阵A^TA接近于单位矩阵(矩阵状态良好)的情况下,未知参数的最小二乘估值是可靠的。但是,在法方程系数阵处于病态的情况下,观测值残差平方和最小并不能保证未知参数估值的方差也小。岭估计能缩短未知参数估值与其真值之间的距离,即减少未知参数估值的方差。

The Ridge Estimation and Its Application

The least squares estimator is a minrmum and unbiased estimator. The parameter estimates are based on the minimum sum of residual spuares. The parameter estimates may be reliable if the coefficient matrix A~TA is nearly a unit matrix. However, minimizing the sum of residual squares may not guarrantee that the variances of the parameter estimates are small if the matrix A~TA is ill-eonditioned. The distances between parameter estimates and their true values may be reduced by using the ridge estimator. In other words, the ridge estimator may be used to improve the accuracies with regard to the parameters of imprecised estimates.