岭回归估计均方误差的重要特性及其应用

THE IMPORTANT PROPERTIES OF MEAN SQUARED ERROR OF RIDGE REGRESSION ESTIMATOR AND IT'S APPLICATIONS

通过深入分析单参数岭估计β（k）的均方误差MSE（β（k），得到了它的一个重要特性。并把较优均方误差的存在范围由（0,σ∧2/maxa∧2γ）扩大到（0.2σ∧2/maxa∧2γ）；同时，还得到了较优均方误差的另一不可替代的存在范围（0，2σ∧2minλγ/（maxλγα∧2γ-σ∧2）；以及最优均方误差的存在范围[σ∧2/maxα∧2γ，σ∧2/minα∧2γ]，并结合实际问题，给出了岭参数k值选的算法实例。

An important property of mean squared error of ridge regression estimator is ob- tamed with an analysis of MSE (β(k)) to the ridge regression estimator β( k) of parameter vector, and the range of a better MSE is expanded from(0. max ) to ( 0.2 max ] .Meanwhile .another range of smaller mean square error that can' t be replaced is proposed and the interval of the minimum MSE value of is aequired. Finally.a practical example is presented with algorithm for choosing the ridge parameter k value.