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We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model.
Modified sequentially rejective multiple test procedures
Shaffer, J. P. (1986) · 1986
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Controlling the false discovery rate: a practical and powerful approach to multiple testing
Benjamini, Y. and Hochberg, Y. (1995) · 1995
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Regression shrinkage and selection via the Lasso
Tibshirani, R. (1996) · 1996
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Gene expression profiling predicts clinical outcome of breast cancer
van ’t Veer, L. J., Dai, H., van de Vijver, M. J., He, Y. D., Hart, A. A. M., Mao, M., Peterse, H. L., van der Kooy, K., Marton, M. J., Witteveen, A. T., Schreiber, G. J., Kerkhoven, R. M., Roberts, C., Linsley, P. S., Bernards, R., and Friend, S. H. (2002) · 2002
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Integrating regulatory motif discovery and genome-wide expression analysis
Conlon, E. M., Liu, X. S., Lieb, J. D., and Liu, J. S. (2003) · 2003
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Testing against a high dimensional alternative
Goeman, J. J., Van De Geer, S. A., and Van Houwelingen, H. C. (2006) · 2006
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Hierarchical testing of variable importance
Meinshausen, N. (2008) · 2008
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The sparsity and bias of the Lasso selection in high-dimensional linear regression
Zhang, C.-H. and Huang, J. (2008) · 2008
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P-values for high-dimensional regression
Meinshausen, N., Meier, L., and Bühlmann, P. (2009) · 2009
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High dimensional variable selection
Wasserman, L. and Roeder, K. (2009) · 2009
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Statistics for High-Dimensional Data: Methods, Theory and Applications
Bühlmann, P. and van de Geer, S. (2011) · 2011
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A perturbation method for inference on regularized regression estimates
Minnier, J., Tian, L., and Cai, T. (2011) · 2011
Cited alongside, same era.
The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso)
van de Geer, S., Bühlmann, P., and Zhou, S. (2011) · 2011
Cited alongside, same era.
Statistical significance in high-dimensional linear models
Bühlmann, P. (2013) · 2013
Cited alongside, same era.
Asymptotic properties of Lasso+mLS and Lasso+Ridge in sparse high-dimensional linear regression
Liu, H. and Yu, B. (2013) · 2013
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Assumption-free confidence intervals for groups of variables in sparse high-dimensional regression
Meinshausen, N. (2013) · 2013
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High-dimensional statistics with a view toward applications in biology
Bühlmann, P., Kalisch, M., and Meier, L. (2014) · 2014
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High-dimensional variable screening and bias in subsequent inference, with an empirical comparison
Bühlmann, P. and Mandozzi, J. (2014) · 2014
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High-dimensional Inference: Confidence intervals, p-values and R-software hdi
Dezeure, R., Bühlmann, P., Meier, L., and Meinshausen, N. (2014) · 2014
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Correlated variables in regression: clustering and sparse estimation (with discussion)
Bühlmann, P., Rütimann, P., van de Geer, S., and Zhang, C.-H. (2013) · 2013
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Rates of convergence of the adaptive Lasso estimators to the oracle distribution and higher order refinements by the bootstrap
Chatterjee, A. and Lahiri, S. N. (2013) · 2013
Cited alongside, same era.
Confidence intervals and hypothesis testing for high-dimensional regression
Javanmard, A. and Montanari, A. (2014a)
Cited in the paper.
Javanmard, A. and Montanari, A. (2014b)
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On asymptotically optimal confidence regions and tests for high-dimensional models
van de Geer, S., Bühlmann, P., Ritov, Y., and Dezeure, R. (2014) · 2014
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Confidence intervals for low dimensional parameters in high dimensional linear models
Zhang, C.-H. and Zhang, S. S. (2014) · 2014
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