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In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models.
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High dimensional variable selection
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Nearly unbiased variable selection under minimax concave penalty
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Restricted eigenvalue properties for correlated gaussian designs
G. Raskutti, M. J. Wainwright, and B. Yu · 2010
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Square-root lasso: pivotal recovery of sparse signals via conic programming
A. Belloni, V. Chernozhukov, and L. Wang · 2011
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Statistics for High-Dimensional data: Methods, Theory and Applications
P. Bühlmann and S. van de Geer · 2011
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A. Chatterjee and S. N. Lahiri · 2011
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A significance test for the lasso
R. Lockhart, J. Taylor, R. J. Tibshirani, and R. Tibshirani · 2014
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Variable selection diagnostics measures for high-dimensional regression
Y. Nan and Y. Yang · 2014
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A general theory of hypothesis tests and confidence regions for sparse high dimensional models
Y. Ning and H. Liu · 2014
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On asymptotically optimal confidence regions and tests for high-dimensional models
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C.-H. Zhang and T. Zhang · 2012
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Scaled sparse linear regression
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C.-H. Zhang and T. Zhang · 2012
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Statistical significance in high-dimensional linear models
P. Bühlmann · 2013
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Variable selection with error control: another look at stability selection
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S. van de Geer, P. Bühlmann, Y. Ritov, and R. Dezeure · 2014
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Inference in high dimensions with the penalized score test
A. Voorman, A. Shojaie, and D. Witten · 2014
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Confidence intervals for low dimensional parameters in high dimensional linear models
C.-H. Zhang and S. S. Zhang · 2014
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Monte carlo simulation for lasso-type problems by estimator augmentation
Q. Zhou · 2014
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Central limit theorems and bootstrap in high dimensions
V. Chernozhukov, D. Chetverikov, and K. Kato · 2014
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Interaction screening for ultrahigh-dimensional data
N. Hao and H. H. Zhang · 2014
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High-dimensional inference in misspecified linear models
P. Bühlmann and S. van de Geer · 2015
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High-dimensional Inference: Confidence intervals, p-values and R-Software hdi
R. Dezeure, P. Bühlmann, L. Meier, and N. Meinshausen · 2015
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Group bound: confidence intervals for groups of variables in sparse high dimensional regression without assumptions on the design
N. Meinshausen · 2015
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Asymptotic normality and optimalities in estimation of large Gaussian graphical models
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Uncertainty quantification under group sparsity
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