Two-parameter ridge regression and its convergence to the eventual pairwise model

Abstract

A generalization of the one-parameter ridge regression to a two-parameter model and its asymptotic behavior, which has various better fitting characteristics, is considered. For the two-parameter model, the coefficients of regression, their t -statistics and net effects, the residual variance and coefficient of multiple determination, the characteristics of bias, efficiency, and generalized cross-validation are very stable and as the ridge parameter increases they eventually reach asymptotic levels. In particular, the beta coefficients of multiple two-parameter ridge regression models converge to a solution proportional to the coefficients of paired regressions. The suggested technique produces robust regression models not prone to multicollinearity, with interpretable coefficients and other characteristics convenient for analysis of the models.