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Rejoinder on: Hierarchical inference for genome-wide association studies: a view on methodology with software

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The Original Article was published on 06 January 2020

The Original Article was published on 06 January 2020

The Original Article was published on 06 January 2020

The Original Article was published on 06 January 2020

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References

  • Angrist J, Imbens G, Rubin D (1996) Identification of causal effects using instrumental variables. J Am Stat Assoc 91:444–455

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Breiman L (1996a) Bagging predictors. Mach Learn 24:123–140

    MATH  Google Scholar 

  • Breiman L (1996b) Heuristics of instability and stabilization in model selection. Ann Stat 24:2350–2383

    Article  MathSciNet  Google Scholar 

  • Bühlmann P, van de Geer S (2011) Statistics for high-dimensional data: methods, theory and applications. Springer, Berlin

    Book  Google Scholar 

  • Buzdugan L, Kalisch M, Navarro A, Schunk D, Fehr E, Bühlmann P (2016) Assessing statistical significance in multivariable genome wide association analysis. Bioinformatics 32:1990–2000

    Article  Google Scholar 

  • Ćevid D, Bühlmann P, Meinshausen N (2018) Spectral deconfounding and perturbed sparse linear models. Preprint arXiv:1811.05352

  • Fithian W, Sun D, Taylor J (2014) Optimal inference after model selection. Preprint arXiv:1410.2597

  • Goeman JJ, Mansmann U (2008) Multiple testing on the directed acyclic graph of gene ontology. Bioinformatics 24:537–544

    Article  Google Scholar 

  • Goeman JJ, Solari A (2014) Multiple hypothesis testing in genomics. Stat Med 33:1946–1978

    Article  MathSciNet  Google Scholar 

  • Guo Z, Renaux C, Bühlmann P, Cai T (2019) Group inference in high dimensions with applications to hierarchical testing. Preprint arXiv:1909.01503

  • Heller R, Yekutieli D (2014) Replicability analysis for genome-wide association studies. Ann Appl Stat 8:481–498

    Article  MathSciNet  Google Scholar 

  • Klasen J, Barbez E, Meier L, Meinshausen N, Bühlmann P, Koornneef M, Busch W, Schneeberger K (2016) A multi-marker association method for genome-wide association studies without the need for population structure correction. Nat Commun. https://doi.org/10.1038/ncomms13299

    Article  Google Scholar 

  • Kumbier K, Yu B (2019) Veridical data science. Preprint arXiv:1901.08152

  • Lockhart R, Taylor J, Tibshirani RJ, Tibshirani R (2014) A significance test for the lasso. Ann Stat 42:413–468

    Article  MathSciNet  Google Scholar 

  • 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 (2008) Hierarchical testing of variable importance. Biometrika 95:265–278

    Article  MathSciNet  Google Scholar 

  • Meinshausen N, Bühlmann P (2010) Stability Selection (with discussion). J R Stat Soc Ser B 72:417–473

    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  Google Scholar 

  • Pan SJ, Yang Q (2010) A survey on transfer learning. IEEE Trans Knowl Data Eng 22:1345–1359

    Article  Google Scholar 

  • Romano J, DiCiccio C (2019) Multiple data splitting for testing. Technical report no. 2019-03, Department of Statistics, Stanford University

  • Rothenhäusler D, Meinshausen N, Bühlmann P, Peters J (2018) Anchor regression: heterogeneous data meets causality. Preprint arXiv:1801.06229

  • Schelldorfer J, Bühlmann P, van de Geer S (2011) Estimation for high-dimensional linear mixed-effects models using \(\ell _1\)-penalization. Scand J Stat 38:197–214

    Article  MathSciNet  Google Scholar 

  • Schelldorfer J, Meier L, Bühlmann P (2014) GLMMLasso: an algorithm for high-dimensional generalized linear mixed models using \(\ell _1\)-penalization. J Comput Graph Stat 23(2):460–477

    Article  Google Scholar 

  • Shah R, Samworth R (2013) Variable selection with error control: another look at Stability Selection. J R Stat Soc Ser B 75:55–80

    Article  MathSciNet  Google Scholar 

  • Spirtes P, Glymour C, Scheines R (2000) Causation, prediction, and search, 2nd edn. MIT Press, Cambridge

    MATH  Google Scholar 

  • Tibshirani R, Taylor J, Lockhart R, Tibshirani R (2016) Exact post-selection inference for sequential regression procedures. J Am Stat Assoc 514:600–620

    Article  MathSciNet  Google Scholar 

  • Tukey J (1954) Causation, regression, and path analysis. In: Kempthorne O (ed) Statistics and mathematics in biology. Iowa State College Press, Ames, pp 35–66

    Google Scholar 

  • van de Geer S (2016) Estimation and Testing Under Sparsity: École d’Été de Probabilités des Saint-Flour XLV – 2015. Lecture notes in mathematics 2159. Springer, Berlin

    Book  Google Scholar 

  • van de Geer S, Bühlmann P, Zhou S (2011) The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso). Electron J Stat 5:688–749

    Article  MathSciNet  Google Scholar 

  • Wang Y, Blei D (2018) The blessings of multiple causes. To appear in J. Amer. Statist. Assoc. Preprint arXiv:1805.06826

  • Yu B (2013) Stability. Bernoulli 19(4):1484–1500

    Article  MathSciNet  Google Scholar 

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Correspondence to Peter Bühlmann.

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This rejoinder refers to the comments available at: 10.1007/s00180-019-00945-4, 10.1007/s00180-019-00941-8, 10.1007/s00180-019-00942-7, 10.1007/s00180-019-00943-6.

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Renaux, C., Buzdugan, L., Kalisch, M. et al. Rejoinder on: Hierarchical inference for genome-wide association studies: a view on methodology with software. Comput Stat 35, 59–67 (2020). https://doi.org/10.1007/s00180-019-00948-1

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