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It is in general challenging to provide confidence intervals for individual variables in high-dimensional regression without making strict or unverifiable assumptions on the design matrix.
Regression shrinkage and selection via the lasso
R. Tibshirani · 1996
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M.R. Osborne, B. Presnell, and B.A. Turlach · 2000
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Atomic decomposition by basis pursuit
S. Chen, S. Donoho, and M. Saunders · 2001
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Least angle regression
B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani · 2004
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Persistence in high-dimensional predictor selection and the virtue of over-parametrization
E. Greenshtein and Y. Ritov · 2004
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R: A language and environment for statistical computing
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The group lasso for logistic regression
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Hierarchical testing of variable importance
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The sparsity and bias of the lasso selection in high-dimensional linear regression
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J. Friedman, T. Hastie, and R. Tibshirani · 2009
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P-values for high-dimensional regression
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K. Soetaert, K. van den Meersche, and D. van Oevelen · 2009
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On the conditions used to prove oracle results for the lasso
S.A. van de Geer and P. Bühlmann · 2009
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L. Wasserman and K. Roeder · 2009
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C.H. Zhang and S. Zhang · 2011
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Statistical significance in high-dimensional linear models
P. Bühlmann · 2012
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Generalized fiducial inference for normal linear mixed models
J. Cisewski and J. Hannig · 2012
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Fiducial prediction intervals
C. Wang, J. Hannig, and H.K. Iyer · 2012
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Confidence intervals and hypothesis testing for high-dimensional regression
A. Javanmard and A. Montanari · 2013
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Stability selection (with discussion)
N. Meinshausen and P. Bühlmann · 2010
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Restricted eigenvalue properties for correlated gaussian designs
G. Raskutti, M. Wainwright, and B. Yu · 2010
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C. Lim and B. Yu · 2013
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A significance test for the lasso
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On asymptotically optimal confidence regions and tests for high-dimensional models
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