Singular Ridge Regression with Homoscedastic Residuals: Generalization Error with Estimated Parameters
24 Pages Posted: 13 Jul 2017
Date Written: May 20, 2016
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.
Keywords: ridge regression, singular regression, training error, testing error, generalization error, regularization methods, high-dimensional regression
JEL Classification: C35, C52
Suggested Citation: Suggested Citation