Condition numbers of the generalized ridge regression and its statistical estimation

Abstract

In this paper, we considered the condition number theory of a new generalized ridge regression model. The explicit expressions of different types of condition numbers were derived to measure the ill-conditionness of the generalized ridge regression problem with respect to different circumstances. To overcome the computational difficulty of computing the exact value of the condition number, we employed the statistical condition estimation theory to design efficient condition number estimators, and the numerical examples were also given to illustrate its efficiency.

Keywords

• ridge regression
• normwise condition number
• mixed and componentwise condition numbers
• statistical condition estimation