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This paper studies schemes to de-bias the Lasso in a linear model $y=X\beta+\epsilon$ where the goal is to construct confidence intervals for $a_0^T\beta$ in a direction $a_0$, where $X$ has iid $N(0,\Sigma)$ rows.
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Cun-Hui Zhang and Tong Zhang, A general theory of concave regularization for high-dimensional sparse estimation problems , Statistical Science 27
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Alexandre Belloni, Victor Chernozhukov, and Lie Wang, Pivotal estimation via square-root lasso in nonparametric regression , Ann. Statist. 42
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Adel Javanmard and Andrea Montanari, Confidence intervals and hypothesis testing for high-dimensional regression , The Journal of Machine Learning Research 15
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Pierre C. Bellec, Optimal bounds for aggregation of affine estimators , Ann. Statist. 46
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Pierre C. Bellec, Guillaume Lecué, and Alexandre B. Tsybakov, Slope meets lasso: Improved oracle bounds and optimality , Ann. Statist. 46
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Yinchu Zhu and Jelena Bradic, Linear hypothesis testing in dense high-dimensional linear models , Journal of the American Statistical Association 113
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Yinchu Zhu, Jelena Bradic, et al., Significance testing in non-sparse high-dimensional linear models , Electronic Journal of Statistics 12
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