Monday, January 10, 2011
Ridge Regression
Ridge Regression projects Y onto principle components, or fits a linear surface over the domain of the PC's. Ridge regression shrinks regression co-efficients with respect to the orthonormal basis formed by the principle components. It is a shrinkage method. In producing the coefficient estimates, a 'penalized' residual sum of squares is minimized.
By its nature, ridge regression addresses multicollinearity. The estimates have increased bias, but lower variance. Ridge regression is an example of a case where a biased estimator can outperform an unbiased estimator given small enough variance (or large enough improvements in efficiency.
By its nature, ridge regression addresses multicollinearity. The estimates have increased bias, but lower variance. Ridge regression is an example of a case where a biased estimator can outperform an unbiased estimator given small enough variance (or large enough improvements in efficiency.
min{e'e + λβ'β) 'penalized residual sum of squares' where λ is a penalty or shrinkage factor
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