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Rejoinder: “A significance test for the lasso”. (English) Zbl 1305.62255
Rejoinder to the comments in [Zbl 1305.62248; Zbl 1305.62250; Zbl 1305.62251; Zbl 1305.62256; Zbl 1305.62257; Zbl 1305.62249] to the authors’ paper [ibid. 42, No. 2, 413–468 (2014; Zbl 1305.62254)].

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
62F03 Parametric hypothesis testing
62J05 Linear regression; mixed models
62J12 Generalized linear models (logistic models)
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[1] Beck, A. and Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2 183-202. · Zbl 1175.94009 · doi:10.1137/080716542
[2] Becker, S., Bobin, J. and Candès, E. J. (2011). NESTA: A fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4 1-39. · Zbl 1209.90265 · doi:10.1137/090756855
[3] Becker, S. R., Candès, E. J. and Grant, M. C. (2011). Templates for convex cone problems with applications to sparse signal recovery. Math. Program. Comput. 3 165-218. · Zbl 1257.90042 · doi:10.1007/s12532-011-0029-5
[4] Boyd, S., Parikh, N., Chu, E., Peleato, B. and Eckstein, J. (2011). Distributed optimization and statistical learning via the alternative direction method of multipliers. Faund. Trends Mach. Learn. 3 1-122. · Zbl 1229.90122 · doi:10.1561/2200000016
[5] Bühlmann, P. (2013). Statistical significance in high-dimensional linear models. Bernoulli 19 1212-1242. · Zbl 1273.62173 · doi:10.3150/12-BEJSP11
[6] Candès, E. J. and Plan, Y. (2009). Near-ideal model selection by \(\ell_1\) minimization. Ann. Statist. 37 2145-2177. · Zbl 1173.62053 · doi:10.1214/08-AOS653
[7] Candes, E. J. and Tao, T. (2006). Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory 52 5406-5425. · Zbl 1309.94033 · doi:10.1109/TIT.2006.885507
[8] Chen, S. S., Donoho, D. L. and Saunders, M. A. (1998). Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20 33-61. · Zbl 0919.94002 · doi:10.1137/S1064827596304010
[9] de Haan, L. and Ferreira, A. (2006). Extreme Value Theory : An Introduction . Springer, New York. · Zbl 1101.62002
[10] Donoho, D. L. (2006). Compressed sensing. IEEE Trans. Inform. Theory 52 1289-1306. · Zbl 1288.94016 · doi:10.1109/TIT.2006.871582
[11] Efron, B. (1986). How biased is the apparent error rate of a prediction rule? J. Amer. Statist. Assoc. 81 461-470. · Zbl 0621.62073 · doi:10.2307/2289236
[12] Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. Ann. Statist. 32 407-499. · Zbl 1091.62054 · doi:10.1214/009053604000000067
[13] Fan, J., Guo, S. and Hao, N. (2012). Variance estimation using refitted cross-validation in ultrahigh-dimensional regression. J. R. Stat. Soc. Ser. B Stat. Methodol. 74 37-65. · doi:10.1111/j.1467-9868.2011.01005.x
[14] Friedman, J., Hastie, T. and Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33 1-22.
[15] Friedman, J., Hastie, T., Höfling, H. and Tibshirani, R. (2007). Pathwise coordinate optimization. Ann. Appl. Stat. 1 302-332. · Zbl 1378.90064 · doi:10.1214/07-AOAS131
[16] Fuchs, J. J. (2005). Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inform. Theory 51 3601-3608. · Zbl 1286.94031 · doi:10.1109/TIT.2005.855614
[17] Grazier G’Sell, M., Taylor, J. and Tibshirani, R. (2013). Adaptive testing for the graphical lasso. Preprint. Available at . · arxiv.org
[18] Grazier G’Sell, M., Wager, S., Chouldechova, A. and Tibshirani, R. (2013). False discovery rate control for sequential selection procedures, with application to the lasso. Preprint. Available at . · arxiv.org
[19] Greenshtein, E. and Ritov, Y. (2004). Persistence in high-dimensional linear predictor selection and the virtue of overparametrization. Bernoulli 10 971-988. · Zbl 1055.62078 · doi:10.3150/bj/1106314846
[20] Hastie, T., Tibshirani, R. and Friedman, J. (2008). The Elements of Statistical Learning ; Data Mining , Inference , and Prediction , 2nd ed. Springer, New York. · Zbl 1273.62005
[21] Javanmard, A. and Montanari, A. (2013a). Confidence intervals and hypothesis testing for high-dimensional regression. Preprint. Available at . · Zbl 1319.62145 · arxiv.org
[22] Javanmard, A. and Montanari, A. (2013b). Hypothesis testing in high-dimensional regression under the Gaussian random design model: Asymptotic theory. Preprint. Available at . · Zbl 1360.62074 · arxiv.org
[23] Meinshausen, N. and Bühlmann, P. (2010). Stability selection. J. R. Stat. Soc. Ser. B Stat. Methodol. 72 417-473. · doi:10.1111/j.1467-9868.2010.00740.x
[24] Meinshausen, N., Meier, L. and Bühlmann, P. (2009). \(p\)-values for high-dimensional regression. J. Amer. Statist. Assoc. 104 1671-1681. · Zbl 1205.62089 · doi:10.1198/jasa.2009.tm08647
[25] Minnier, J., Tian, L. and Cai, T. (2011). A perturbation method for inference on regularized regression estimates. J. Amer. Statist. Assoc. 106 1371-1382. · Zbl 1323.62076 · doi:10.1198/jasa.2011.tm10382
[26] Osborne, M. R., Presnell, B. and Turlach, B. A. (2000a). A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20 389-403. · Zbl 0962.65036 · doi:10.1093/imanum/20.3.389
[27] Osborne, M. R., Presnell, B. and Turlach, B. A. (2000b). On the LASSO and its dual. J. Comput. Graph. Statist. 9 319-337.
[28] Park, M. Y. and Hastie, T. (2007). \(L_1\)-regularization path algorithm for generalized linear models. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 659-677. · doi:10.1111/j.1467-9868.2007.00607.x
[29] Rhee, S.-Y., Gonzales, M. J., Kantor, R., Betts, B. J., Ravela, J. and Shafer, R. W. (2003). Human immunodeficiency virus reverse transcriptase and protease sequence database. Nucleic Acids Res. 31 298-303.
[30] Sun, T. and Zhang, C.-H. (2012). Scaled sparse linear regression. Biometrika 99 879-898. · Zbl 1452.62515 · doi:10.1093/biomet/ass043
[31] Taylor, J., Loftus, J. and Tibshirani, R. J. (2013). Tests in adaptive regression via the Kac-Rice formula. Preprint. Available at . · Zbl 1337.62304 · arxiv.org
[32] Taylor, J., Takemura, A. and Adler, R. J. (2005). Validity of the expected Euler characteristic heuristic. Ann. Probab. 33 1362-1396. · Zbl 1083.60031 · doi:10.1214/009117905000000099
[33] Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267-288. · Zbl 0850.62538
[34] Tibshirani, Ryan J. (2013). The lasso problem and uniqueness. Electron. J. Stat. 7 1456-1490. · Zbl 1337.62173 · doi:10.1214/13-EJS815
[35] Tibshirani, R. J. and Taylor, J. (2012). Degrees of freedom in lasso problems. Ann. Statist. 40 1198-1232. · Zbl 1274.62469 · doi:10.1214/12-AOS1003
[36] van de Geer, S. and Bühlmann, P. (2013). On asymptotically optimal confidence regions and tests for high-dimensional models. Preprint. Available at . · Zbl 1432.62112 · doi:10.1016/j.jspi.2013.03.006 · arxiv.org
[37] Wainwright, M. J. (2009). Sharp thresholds for high-dimensional and noisy sparsity recovery using \(\ell_1\)-constrained quadratic programming (Lasso). IEEE Trans. Inform. Theory 55 2183-2202. · Zbl 1367.62220 · doi:10.1109/TIT.2009.2016018
[38] Wasserman, L. and Roeder, K. (2009). High-dimensional variable selection. Ann. Statist. 37 2178-2201. · Zbl 1173.62054 · doi:10.1214/08-AOS646
[39] Weissman, I. (1978). Estimation of parameters and large quantiles based on the \(k\) largest observations. J. Amer. Statist. Assoc. 73 812-815. · Zbl 0397.62034 · doi:10.2307/2286285
[40] Zhang, C.-H. and Zhang, S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. J. R. Stat. Soc. Ser. B Stat. Methodol. 76 217-242. · doi:10.1111/rssb.12026
[41] Zhao, P. and Yu, B. (2006). On model selection consistency of Lasso. J. Mach. Learn. Res. 7 2541-2563. · Zbl 1222.62008 · www.jmlr.org
[42] Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B Stat. Methodol. 67 301-320. · Zbl 1069.62054 · doi:10.1111/j.1467-9868.2005.00503.x
[43] Zou, H., Hastie, T. and Tibshirani, R. (2007). On the “degrees of freedom” of the lasso. Ann. Statist. 35 2173-2192. · Zbl 1126.62061 · doi:10.1214/009053607000000127 · euclid:aos/1194461726
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