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Comments on: High-dimensional simultaneous inference with the bootstrap

Author

Listed:
  • Richard A. Lockhart

    (Simon Fraser University)

  • Richard J. Samworth

    (University of Cambridge)

Abstract

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.

Suggested Citation

  • Richard A. Lockhart & Richard J. Samworth, 2017. "Comments on: High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 734-739, December.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0555-1
    DOI: 10.1007/s11749-017-0555-1
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    References listed on IDEAS

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    1. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    2. Richard Samworth, 2003. "A note on methods of restoring consistency to the bootstrap," Biometrika, Biometrika Trust, vol. 90(4), pages 985-990, December.
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    Cited by:

    1. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "Rejoinder on: High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 751-758, December.

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