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.