Ellipsoidal Restriction and Generalized Ridge Estimation

Consider the linear regression model \undersetn \times 1Y=\undersetn \times q_q \times 1X+\undersetn \times 1e, \quad e \sim\left(0, \sigma^2 W\right), W>0, \operatornamerank(X)=q. In term of the approximate multicollinearity of matrix X, paper constrains the regression coefficient β and obtains generalized ridge estimation of the linear model’s parameter under the ellipsoidal restriction. Then discusses its properties, such as biased property, and MDE - superiority comparisons between generalized ridge estimation and generalized least squares estimation.