A Method to Determine the Ridge Parameter in Ridge Regression

In this paper, the author considers linear model Y_n \times 1=X_n \times m \beta_m \times 1+\varepsilon_n \times 1, \quad \mathrmE(Y)=X \beta, \quad \operatornameVar(Y)=\sigma^2 I_n, \quad R(X)=m Its canonical model is Y_n \times 1=Z_n \times m \dot\alpha_m \times 1+\varepsilon_n \times 1,, where Z^\prime Z=\Lambda=\operatornamediag\left(\lambda_1, \cdots, \lambda_m\right), \lambda_1 \geq 0, \cdots, \lambda_m \geq 0 are the eigenvalues of X’X, The ridge estimator of α is \widehat\alpha(k)=(\Lambda+k I)^-1 Z^\prime Y and the ridge estimator of β is P’^a（k）, where P is orthogonal matrix. So that P’X’XP = ∧. In this paper, a new method to determine ridge parameter k in ridge regression is given. This method has improved the Hoerl-Kennard formula.