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Optimization of Generalized \(C_p\) Criterion for Selecting Ridge Parameters in Generalized Ridge Regression

  • Mineaki OhishiEmail author
  • Hirokazu Yanagihara
  • Hirofumi Wakaki
Conference paper
  • 60 Downloads
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 193)

Abstract

In a generalized ridge (GR) regression, since a GR estimator (GRE) depends on ridge parameters, it is important to select those parameters appropriately. Ridge parameters selected by minimizing the generalized \(C_p\) (\(GC_p\)) criterion can be obtained as closed forms. However, because the ridge parameters selected by this criterion depend on a nonnegative value \(\alpha \) expressing the strength of the penalty for model complexity, \(\alpha \) must be optimized for obtaining a better GRE. In this paper, we propose a method for optimizing \(\alpha \) in the \(GC_p\) criterion using [12] as similar as [7].

Keywords

Generalized \(C_p\) criterion Generalized ridge regression Ridge parameters Stein’s lemma 

Notes

Acknowledgements

The authors thank the associate editor and the two reviewers for their valuable comments.

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Hiroshima UniversityHigashi-HiroshimaJapan

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