The Ridge Estimation and Its Application

The least squares estimator is a minimum 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-conditioned.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.