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Rejoinder on: High-dimensional simultaneous inference with the bootstrap

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We thank the discussants for their interesting, inspiring and thoughtful comments and ideas. We provide here some responses.

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References

  • Bang H, Robins J (2005) Doubly robust estimation in missing data and causal inference models. Biometrics 61:962–972

    Article  MathSciNet  MATH  Google Scholar 

  • Benjamini Y, Yekutieli D (2005) False discovery rate-adjusted multiple confidence intervals for selected parameters. J Am Stat Assoc 100:71–81

    Article  MathSciNet  MATH  Google Scholar 

  • Berk R, Brown L, Buja A, Zhang K, Zhao L (2013) Valid postselection inference. Ann Stat 41:802–837

    Article  MATH  Google Scholar 

  • Bradic J, Zhu Y (2017) Comments on: high-dimensional simultaneous inference with the bootstrap. TEST. doi:10.1007/s11749-017-0556-0

  • Bühlmann P (2013) Statistical significance in high-dimensional linear models. Bernoulli 19:1212–1242

    Article  MathSciNet  MATH  Google Scholar 

  • Chatterjee A (2017) Comments on: high-dimensional simultaneous inference with the bootstrap. TEST. doi:10.1007/s11749-017-0557-z

  • Dezeure R, Bühhlmann P, Zhang CH (2017) High-dimensional simultaneous inference with the bootstrap (with discussion). TEST. doi:10.1007/s11749-017-0554-2

  • Dezeure R, Bühlmann P, Meier L, Meinshausen N (2015) High-dimensional inference: confidence intervals, \(p\) values and R-software hdi. Stat Sci 30:533–558

    Article  MathSciNet  Google Scholar 

  • Hall P (1988) Theoretical comparison of bootstrap confidence intervals. Ann Stat 16:927–953

    Article  MathSciNet  MATH  Google Scholar 

  • Javanmard A, Montanari A (2014) Confidence intervals and hypothesis testing for high-dimensional regression. J Mach Learn Res 15:2869–2909

    MathSciNet  MATH  Google Scholar 

  • Lee JD, Sun DL, Sun Y, Taylor JE (2016) Exact post-selection inference, with application to the lasso. Ann Stat 44:907–927

    Article  MathSciNet  MATH  Google Scholar 

  • Liu H, Yu B (2013) Asymptotic properties of lasso+mls and lasso+ridge in sparse high-dimensional linear regression. Electron J Stat 7:3124–3169

    Article  MathSciNet  MATH  Google Scholar 

  • Liu H, Yu B (2017) Comments on: high-dimensional simultaneous inference with the bootstrap. TEST. doi:10.1007/s11749-017-0559-x

  • Lockhart R, Samworth R (2017) Comments on: high-dimensional simultaneous inference with the bootstrap. TEST. doi:10.1007/s11749-017-0555-1

  • Löffler M, Nickl R (2017) Comments on: high-dimensional simultaneous inference with the bootstrap. TEST. doi:10.1007/s11749-017-0558-y

  • Mandozzi J, Bühlmann P (2016a) Hierarchical testing in the high-dimensional setting with correlated variables. J Am Stat Assoc 111:331–343

    Article  MathSciNet  Google Scholar 

  • Mandozzi J, Bühlmann P (2016b) A sequential rejection testing method for high-dimensional regression with correlated variables. Int J Biostat 12:79–95

    Article  MathSciNet  Google Scholar 

  • Meinshausen N, Meier L, Bühlmann P (2009) \(P\) values for high-dimensional regression. J Am Stat Assoc 104:1671–1681

    Article  MathSciNet  MATH  Google Scholar 

  • Mitra R, Zhang C-H (2016) The benefit of group sparsity in group inference with de-biased scaled group Lasso. Electron J Stat 10:1829–1873

    Article  MathSciNet  MATH  Google Scholar 

  • Scharfstein D, Rotnitzky A, Robins J (1999) Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussion). J Am Stat Assoc 94:1096–1146

    Article  MATH  Google Scholar 

  • van de Geer S, Bühlmann P, Ritov Y, Dezeure R (2014) On asymptotically optimal confidence regions and tests for high-dimensional models. Ann Stat 42:1166–1202

    Article  MathSciNet  MATH  Google Scholar 

  • van de Geer S, Stucky B (2016) \(\chi ^2\)-confidence sets in high-dimensional regression. In: Frigessi A, Bühlmann P, Glad IK, Langaas M, Richardson S, Vannucci M (eds) Statistical analysis for high-dimensional data, the abel symposium 2014. Springer, New York, pp 279–306

    Google Scholar 

  • Zhang C-H, Zhang SS (2014) Confidence intervals for low dimensional parameters in high dimensional linear models. J Roy Stat Soc B 76:217–242

    Article  MathSciNet  Google Scholar 

  • Zhang X, Cheng G (2016) Simultaneous inference for high-dimensional linear models. J Am Stat Assoc. doi:10.1080/01621459.2016.1166114

    Google Scholar 

  • Zhu Y, Bradic J (2016) Hypothesis testing in non-sparse high-dimensional linear models. arXiv:1610.02122

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Author information

Authors and Affiliations

  1. Seminar for Statistics, ETH Zürich, HG G17, Rämistrasse 101, 8092, Zurich, Switzerland

    Ruben Dezeure & Peter Bühlmann

  2. Department of Statistics and Biostatistics, Rutgers University, 569 Hill Center, Busch Campus, Piscataway, NJ, 08854-8019, USA

    Cun-Hui Zhang

Authors
  1. Ruben Dezeure
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  2. Peter Bühlmann
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  3. Cun-Hui Zhang
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Corresponding author

Correspondence to Peter Bühlmann.

Additional information

Ruben Dezeure is partially supported by the Swiss National Science Foundation SNF 2-77991-14. Cun-Hui Zhang is partially supported by NSF Grants IIS-140793, DMS-15-13378 and DMS-17-21495.

This rejoinder refers to the comments available at doi:10.1007/s11749-017-0555-1; doi: 10.1007/s11749-017-0556-0; doi:10.1007/s11749-017-0557-z; doi: 10.1007/s11749-017-0558-y; doi:10.1007/s11749-017-0559-x.

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Dezeure, R., Bühlmann, P. & Zhang, CH. Rejoinder on: High-dimensional simultaneous inference with the bootstrap. TEST 26, 751–758 (2017). https://doi.org/10.1007/s11749-017-0560-4

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  • DOI: https://doi.org/10.1007/s11749-017-0560-4

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