  This paper characterizes the conditional distribution properties of the
finite sample ridge regression estimator and uses that result to evaluate total
regression and generalization errors that incorporate the inaccuracies
committed at the time of parameter estimation. The paper provides explicit
formulas for those errors. Unlike other classical references in this setup, our
results take place in a fully singular setup that does not assume the existence
of a solution for the non-regularized regression problem. In exchange, we
invoke a conditional homoscedasticity hypothesis on the regularized regression
residuals that is crucial in our developments.
