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This paper considers point and interval estimation of the $\ell_q$ loss of an estimator in high-dimensional linear regression with random design.
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Yuri I Ingster, Alexandre B Tsybakov, and Nicolas Verzelen · 2010
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Rate minimaxity of the lasso and dantzig selector for the ℓ q \ell_{q} loss in ℓ r \ell_{r} balls
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Adaptive confidence bands for nonparametric regression functions
T Tony Cai, Mark G Low, and Zongming Ma · 2014
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On asymptotically optimal confidence regions and tests for high-dimensional models
Sara van de Geer, Peter Bühlmann, YaÕacov Ritov, and Ruben Dezeure · 2014
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Post-selection and post-regularization inference in linear models with many controls and instruments
Victor Chernozhukov, Christian Hansen, and Martin Spindler · 2015
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Valid post-selection and post-regularization inference: An elementary, general approach
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