A bootstrap recipe for post-model-selection inference under linear regression models. (25th September 2018)

• Record Type: Journal Article
• Authors: Lee, S M S; Wu, Y
• Is Part Of: Biometrika. Volume 105:Number 4(2018:Dec.)
• Page Start: 873
• Page End: 890
• Publication Date: 2018-09-25
• Subjects: Bootstrap -- Least squares estimator -- Post-model-selection -- Regression; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asy046
• Languages: English
• ISSNs: 0006-3444

Abstract

SUMMARY: We propose a general bootstrap recipe for estimating the distributions of post-model-selection least squares estimators under a linear regression model. The recipe constrains residual bootstrapping within the most parsimonious, approximately correct, models to yield a distribution estimator which is consistent provided any wrong candidate model is sufficiently separated from the approximately correct ones. Our theory applies to a broad class of model selection methods based on information criteria or sparse estimation. The empirical performance of our procedure is illustrated with simulated data.