A Risk Comparison of Ordinary Least Squares vs Ridge Regression
  We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression. 
Paramveer S. Dhillon, Dean P. Foster, Sham M. Kakade and Lyle H. Ungar
stat.ML