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We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression.
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[author] Huang, JianJ., Breheny, PatrickP. and Ma, ShuanggeS. (2012). A selective review of group selection in high-dimensional models. Statistical Science 27 481-499
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[author] Bühlmann, PeterP. (2013). Statistical significance in high-dimensional linear models. Bernoulli 19 1212–1242
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[author] Cai, T.T., Wang, L.L. and Xu, G.G. (2010). Shifting inequality and recovery of sparse signals. IEEE Transactions on Signal Processing 58 1300–1308
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[author] Meinshausen, NicolaiN. and Bühlmann, PeterP. (2010). Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 417–473
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[author] Ye, FeiF. and Zhang, Cun-HuiC.-H. (2010). Rate Minimaxity of the Lasso and Dantzig Selector for the lq Loss in lr Balls. The Journal of Machine Learning Research 11 3519–3540
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[author] Zhang, Cun-HuiC.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 894–942
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[author] Belloni, AlexandreA., Chernozhukov, VictorV. and Wang, LieL. (2011). Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming. Biometrika 98 791-806
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[author] Shah, Rajen DR. D. and Samworth, Richard JR. J. (2013). Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 75 55–80
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[author] Sun, TingniT. and Zhang, Cun-HuiC.-H. (2013). Sparse matrix inversion with scaled Lasso. Journal of Machine Learning Research 14 3385-3418
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[author] Belloni, AlexandreA., Chernozhukov, VictorV. and Hansen, ChristianC. (2014). Inference on Treatment Effects after Selection among High-Dimensional Controls. The Review of Economic Studies 81 608–650
2014
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[author] Bunea, FlorentinaF., Lederer, JohannesJ. and She, YiyuanY. (2014). The group square-root lasso: Theoretical properties and fast algorithms. Information Theory, IEEE Transactions on 60 1313–1325
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2014
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2014
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[author] Lockhart, RichardR., Taylor, JonathanJ., Tibshirani, Ryan J.R. J. and Tibshirani, RobertR. (2014). A significance test for the lasso. The Annals of Statistics 42 413–468
2014
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[author] Meinshausen, NicolaiN. (2014). Group bound: confidence intervals for groups of variables in sparse high dimensional regression without assumptions on the design. Journal of the Royal Statistical Society: Series B (Statistical Methodology)
2014
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[author] van de Geer, SaraS. (2014). Worst possible sub-directions in high-dimensional models. Contributions in infinite-dimensional statistics and related topics 131
2014
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[author] van de Geer, SaraS., Bühlmann, PeterP., Ritov, Ya’acovY. and Dezeure, RubenR. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics 42 1166–1202
2014
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