A Confidence Bound Approach to Choosing the Biasing Parameter in Ridge Regression
针对多重线性回归中设计矩阵病态的问题，提出一种基于置信界的方法来选择岭回归中的偏置参数k，使得估计量的均方误差小于普通最小二乘估计。
Abstract Consider the multiple linear regression model Y = Xβ + ∈, ∈ ∼ Ň(0, σ2 I) where the matrix S = X' X is ill conditioned. A confidence bound approach is developed for choosing k in the ridge estimator β*(k) = (S + kI)–1 X' Y as follows: A parameter is defined that is essentially the largest (constant) k one could use and still have β*(k)'s mean squared error (MSE) be less than MSE (where is the usual estimate of β). A procedure is then developed to obtain a lower confidence bound k γ for , and the estimator β* ≡ β*(k γ) is considered.