TY - JOUR
T1 - A confidence bound approach to choosing the biasing parameter in ridge regression
AU - Oman, Samuel D.
PY - 1981/6
Y1 - 1981/6
N2 - Consider the multiple linear regression model Y = Xβ + ∈, ∈ ∼ Ň(0, σ2I) 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)–1X’ Y as follows: A parameter (Equation presented) 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 (Equation presented) MSE (where (Equation presented) is the usual estimate of β). A procedure is then developed to obtain a lower confidence bound kγfor (Equation presented), and the estimator β* ≡ β*(kγ) is considered.
AB - Consider the multiple linear regression model Y = Xβ + ∈, ∈ ∼ Ň(0, σ2I) 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)–1X’ Y as follows: A parameter (Equation presented) 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 (Equation presented) MSE (where (Equation presented) is the usual estimate of β). A procedure is then developed to obtain a lower confidence bound kγfor (Equation presented), and the estimator β* ≡ β*(kγ) is considered.
KW - Multiple linear regression: Multicollinearity
KW - Ridge regression
UR - http://www.scopus.com/inward/record.url?scp=80053906658&partnerID=8YFLogxK
U2 - 10.1080/01621459.1981.10477667
DO - 10.1080/01621459.1981.10477667
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AN - SCOPUS:80053906658
SN - 0162-1459
VL - 76
SP - 452
EP - 461
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 374
ER -