Fixed-Size Confidence Regions in High-Dimensional Sparse Linear Regression Models

Abstract

There is an extensive literature on fixed-size confidence regions for the regression parameters in a linear model with p regressors, attaining a prescribed coverage probability when p is fixed and the size d approaches 0. Motivated by recent developments in regression modeling in response to applications for which p is considerably larger than the sample size, we develop herein a more versatile sequential methodology for fixed-size confidence regions that can handle the case p = p(d) → ∞ as d → 0.

Keywords:

• Fixed-width confidence intervals
• High-dimensional information criterion
• Orthogonal greedy algorithm
• Two-stage procedure
• Variable selection

Subject Classifications:

• 62L10
• 62J05
• 62L15
• 62F25

ACKNOWLEDGMENTS

The authors thank Hsiang-Ling Hsu for her assistance in preparing this article and the reviewer and Associate Editor for helpful comments.

Notes

Recommended by Nitis Mukhopadhyay