A confidence bound approach to choosing the biasing parameter in ridge regression

Samuel D. Oman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)452-461
Number of pages10
JournalJournal of the American Statistical Association
Volume76
Issue number374
DOIs
StatePublished - Jun 1981

Keywords

  • Multiple linear regression: Multicollinearity
  • Ridge regression

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