A Bayesian approach with generalized ridge estimation for high-dimensional regression and testing

ABSTRACT

This paper adopts a Bayesian strategy for generalized ridge estimation for high-dimensional regression. We also consider significance testing based on the proposed estimator, which is useful for selecting regressors. Both theoretical and simulation studies show that the proposed estimator can simultaneously outperform the ordinary ridge estimator and the LSE in terms of the mean square error (MSE) criterion. The simulation study also demonstrates the competitive MSE performance of our proposal with the Lasso under sparse models. We demonstrate the method using the lung cancer data involving high-dimensional microarrays.

KEYWORDS:

• Bayes estimator
• Compound covariate estimator
• Linear model
• Mean square error
• Shrinkage estimator
• Statistical decision theory

Acknowledgements

We thank the anonymous reviewers for their helpful comments that improve the manuscript. We are also thankful to Prof. Tsai-Hung Fan, Dr. Chen Yi-Hau and Prof. Sheng-Mao Chang for their comments on an earlier version of our paper. This work was financially supported by the National Science Council of Taiwan (NSC101-2118-M008-002-MY2).