Applications of the jackknife procedure in ridge regression

Abstract

Three aspects of the application of the jackknife technique to ridge regression are considered, viz. as a bias estimator, as a variance estimator, and as an indicator of observations influence on parameter estimates. The ridge parameter is considered non-stochastic. The jackknifed ridge estimator is found to be a ridge estimator with a smaller value on the ridge parameter. Hence it has a smaller bias but a larger variance than the ridge estimator. The variance estimator is expected to be robust against heteroscedastic error variance as well as against outliers. A measure of observations influence on the estimates of regression parameters is proposed.