Abstract
We provide comments on the article “High-dimensional simultaneous inference with the bootstrap” by Ruben Dezeure, Peter Buhlmann and Cun-Hui Zhang.
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In 1950s, many statisticians including Jack Kiefer, Herbert Robbins, Jack Wolfowitz, R. C. Bose, Abraham Wald and Milton Sobel thought that the area of ranking and selection is a “revolution”.
In paper (2010), Chatterjee and Lahiri showed that bootstrapping the Lasso is inconsistent whenever one or more regression coefficients are zero. They proposed bootstrapping the thresholded Lasso (Chatterjee and Lahiri 2011) and bootstrapping the adaptive Lasso (Chatterjee and Lahiri 2013) and showed their validation under the beta-min condition and other appropriate conditions. However, bootstrapping the Lasso performs comparably (but is simpler) to the other two methods in simulations where the signal-to-noise ratio is not high.
References
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Acknowledgements
We would like to thank the Editor for the invitation to discuss and thank the Gallant Lab at UC Berkeley for providing the fMRI data. We also thank Jasjeet Sekhon for helpful discussions and for comments that clarify the text and thank Rebecca Barter for extremely helpful comments that led to much improvement of the paper.
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This work is supported in part by NSF Grant DMS-1228246, ONR Grant N00014-16-1-2664, AFOSR Grant FA9550-14-1-0016, and by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under Grant Agreement CCF-0939370 (to Yu).
This comment refers to the invited paper available at: doi:10.1007/s11749-017-0554-2.
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Liu, H., Yu, B. Comments on: High-dimensional simultaneous inference with the bootstrap. TEST 26, 740–750 (2017). https://doi.org/10.1007/s11749-017-0559-x
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DOI: https://doi.org/10.1007/s11749-017-0559-x
Keywords
- Ranking and selection
- Mean squared error
- Coverage
- High-dimensional statistical inference
- Bootstrapping LassoOLS