Penalized Maximum Likelihood Principle for Choosing Ridge Parameter

Abstract

We consider the problem of choosing the ridge parameter. Two penalized maximum likelihood (PML) criteria based on a distribution-free and a data-dependent penalty function are proposed. These PML criteria can be considered as “continuous” versions of AIC. A systematic simulation is conducted to compare the suggested criteria to several existing methods. The simulation results strongly support the use of our method. The method is also applied to two real data sets.

Keywords:

• Data-dependent penalty
• Loss rank principle
• Model selection
• Penalized ML
• Ridge parameter
• Ridge regression

Mathematics Subject Classification:

• 62J07
• 62J05

Acknowledgment

The author would like to thank the Associate Editor and the reviewer for their careful reading and helpful comments.