Comments on: High-dimensional simultaneous inference with the bootstrap

We congratulate the authors on their stimulating contribution to the burgeoning high-dimensional inference literature. The bootstrap offers such an attractive methodology in these settings, but it is well-known that its naive application in the context of shrinkage/superefficiency is fraught with da...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2017-12, Vol.26 (4), p.734-739
Main Authors: Lockhart, Richard A., Samworth, Richard J.
Format: Article
Language:English
Subjects:
Bootstrap method
Confidence intervals
Discussion
Economics
Finance
Hazards
Inference
Insurance
Management
Mathematics and Statistics
Shrinkage
Statistical Theory and Methods
Statistics
Statistics for Business
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Summary:We congratulate the authors on their stimulating contribution to the burgeoning high-dimensional inference literature. The bootstrap offers such an attractive methodology in these settings, but it is well-known that its naive application in the context of shrinkage/superefficiency is fraught with danger (e.g. Samworth in Biometrika 90:985–990, 2003 ; Chatterjee and Lahiri in J Am Stat Assoc 106:608–625, 2011 ). The authors show how these perils can be elegantly sidestepped by working with de-biased, or de-sparsified, versions of estimators. In this discussion, we consider alternative approaches to individual and simultaneous inference in high-dimensional linear models, and retain the notation of the paper.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-017-0555-1