Journal article

A Confidence Region Approach to Tuning for Variable Selection

Funda Gunes, Howard D Bondell

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS | AMER STATISTICAL ASSOC | Published : 2012

Abstract

We develop an approach to tuning of penalized regression variable selection methods by calculating the sparsest estimator contained in a confidence region of a specified level. Because confidence intervals/regions are generally understood, tuning penalized regression methods in this way is intuitive and more easily understood by scientists and practitioners. More importantly, our work shows that tuning to a fixed confidence level often performs better than tuning via the common methods based on AIC, BIC, or cross-validation (CV) over a wide range of sample sizes and levels of sparsity. Additionally, we prove that by tuning with a sequence of confidence levels converging to one, asymptotic se..

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Funding Acknowledgements

The authors are grateful to Len Stefanski for helpful discussions during the preparation of the article. The authors thank the editor, associate editor, and three referees for their helpful comments that improved the manuscript. This work was partially supported by NSF grant DMS-1005612 and NIH grants R01 MH-084022 and P01 CA-142538.