# Ridge regression and its degrees of freedom

Ridge regression and its degrees of freedom For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter is optimized on the same data, by minimization of the generalized cross validation criterion or Mallows $$\hbox {C}_{L}$$ C L , additional degrees of freedom are used however. We give formulae that take this into account. This allows of a proper assessment of ridge regression in competitions for the best predictor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

# Ridge regression and its degrees of freedom

, Volume 48 (6) – Oct 25, 2013
9 pages

/lp/springer_journal/ridge-regression-and-its-degrees-of-freedom-m35QXZA3eP
Publisher
Springer Journals
Subject
Social Sciences, general; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-013-9949-7
Publisher site
See Article on Publisher Site

### Abstract

For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter is optimized on the same data, by minimization of the generalized cross validation criterion or Mallows $$\hbox {C}_{L}$$ C L , additional degrees of freedom are used however. We give formulae that take this into account. This allows of a proper assessment of ridge regression in competitions for the best predictor.

### Journal

Quality & QuantitySpringer Journals

Published: Oct 25, 2013

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