{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T03:05:21Z","timestamp":1783652721583,"version":"3.55.0"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:00Z","timestamp":1557878400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:00Z","timestamp":1557878400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s00211-019-01051-9","type":"journal-article","created":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T06:02:23Z","timestamp":1557900143000},"page":"667-711","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Correcting for unknown errors in sparse high-dimensional function approximation"],"prefix":"10.1007","volume":"142","author":[{"given":"Ben","family":"Adcock","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anyi","family":"Bao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simone","family":"Brugiapaglia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,5,15]]},"reference":[{"key":"1051_CR1","unstructured":"Adcock, B.: Infinite-dimensional compressed sensing and function interpolation. Found. Comput. Math. 18(3), 661\u2013701 (2018)"},{"issue":"3","key":"1051_CR2","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/s00365-017-9369-3","volume":"45","author":"B Adcock","year":"2017","unstructured":"Adcock, B.: Infinite-dimensional $$\\ell ^1$$ minimization and function approximation from pointwise data. Constr. Approx. 45(3), 345\u2013390 (2017)","journal-title":"Constr. Approx."},{"key":"1051_CR3","unstructured":"Adcock, B., Bao, A., Narayan, A., Author, U.: Compressed sensing with sparse corruptions: fault-tolerant sparse collocation approximations (2017). arXiv:1703.00135"},{"key":"1051_CR4","unstructured":"Adcock, B., Brugiapaglia, S., Webster, C.G.: Compressed sensing approaches for polynomial approximation of high-dimensional functions (2017). arXiv:1703.06987"},{"key":"1051_CR5","doi-asserted-by":"publisher","unstructured":"Adcock, B., Hansen, A.C., Poon, C., Roman, B.: Breaking the coherence barrier: a new theory for compressed sensing. Forum Math. Sigma 5, E4. (2017). https:\/\/doi.org\/10.1017\/fms.2016.32","DOI":"10.1017\/fms.2016.32"},{"key":"1051_CR6","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/09-SS054","volume":"4","author":"S Arlot","year":"2010","unstructured":"Arlot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40\u201379 (2010)","journal-title":"Stat. Surv."},{"issue":"6","key":"1051_CR7","doi-asserted-by":"publisher","first-page":"1952","DOI":"10.1016\/j.csda.2011.11.022","volume":"56","author":"O Arslan","year":"2012","unstructured":"Arslan, O.: Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression. Comput. Stat. Data Anal. 56(6), 1952\u20131965 (2012)","journal-title":"Comput. Stat. Data Anal."},{"key":"1051_CR8","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.sigpro.2013.08.011","volume":"95","author":"P Babu","year":"2014","unstructured":"Babu, P., Stoica, P.: Connection between spice and square-root lasso for sparse parameter estimation. Signal Process. 95, 10\u201314 (2014)","journal-title":"Signal Process."},{"key":"1051_CR9","doi-asserted-by":"crossref","unstructured":"B\u00e4ck, J., Nobile, F., Tamellini, L., Tempone, R.: Stochastic spectral galerkin and collocation methods for pdes with random coefficients: A numerical comparison. In: Hesthaven, J.S., R\u00f8nquist, E.M. (eds.) Spectral and High Order Methods for Partial Differential Equations: Selected Papers from the ICOSAHOM \u201909 Conference. June 22\u201326, Trondheim, Norway, pp. 43\u201362. Springer, Berlin (2011)","DOI":"10.1007\/978-3-642-15337-2_3"},{"issue":"1","key":"1051_CR10","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1137\/140960980","volume":"3","author":"J Ballani","year":"2015","unstructured":"Ballani, J., Grasedyck, L.: Hierarchical tensor approximation of output quantities of parameter-dependent pdes. SIAM\/ASA J. Uncertain. Quantif. 3(1), 852\u2013872 (2015)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"1051_CR11","unstructured":"Bastounis, A., Hansen, A.C.: On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels (2014). arXiv:1411.4449"},{"issue":"4","key":"1051_CR12","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1093\/biomet\/asr043","volume":"98","author":"A Belloni","year":"2011","unstructured":"Belloni, A., Chernozhukov, V., Wang, L.: Square-root lasso: pivotal recovery of sparse signals via conic programming. Biometrika 98(4), 791\u2013806 (2011)","journal-title":"Biometrika"},{"issue":"2","key":"1051_CR13","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1214\/14-AOS1204","volume":"42","author":"A Belloni","year":"2014","unstructured":"Belloni, A., Chernozhukov, V., Wang, L.: Pivotal estimation via square-root lasso in nonparametric regression. Ann. Stat. 42(2), 757\u2013788 (2014)","journal-title":"Ann. Stat."},{"key":"1051_CR14","unstructured":"Bridges, P.G., Ferreira, K.B., Heroux, M.A., Hoemmen, M.: Fault-tolerant linear solvers via selective reliability (2012). arXiv:1206.1390"},{"key":"1051_CR15","unstructured":"Brugiapaglia, S., Adcock, B.: Robustness to unknown error in sparse regularization (2017). arXiv:1705.10299"},{"key":"1051_CR16","doi-asserted-by":"crossref","unstructured":"Brugiapaglia, S., Adcock, B., Archibald, R.K.: Recovery guarantees for compressed sensing with unknown errors. In: 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE (2017)","DOI":"10.1109\/SAMPTA.2017.8024421"},{"issue":"2","key":"1051_CR17","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1109\/TIT.2013.2290040","volume":"60","author":"F Bunea","year":"2014","unstructured":"Bunea, F., Lederer, J., She, Y.: The group square-root lasso: theoretical properties and fast algorithms. IEEE Trans. Inform. Theory 60(2), 1313\u20131325 (2014)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"1051_CR18","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52(2), 489\u2013509 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"5","key":"1051_CR19","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","volume":"14","author":"EJ Cand\u00e8s","year":"2008","unstructured":"Cand\u00e8s, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted $$\\ell ^1$$ minimization. J. Fourier Anal. Appl. 14(5), 877\u2013905 (2008)","journal-title":"J. Fourier Anal. Appl."},{"issue":"3","key":"1051_CR20","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1051\/m2an\/2014050","volume":"49","author":"A Chkifa","year":"2015","unstructured":"Chkifa, A., Cohen, A., Migliorati, G., Nobile, F., Tempone, R.: Discrete least squares polynomial approximation with random evaluations\u2014application to parametric and stochastic elliptic pdes. ESAIM Math. Model. Numer. Anal. 49(3), 815\u2013837 (2015)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"4","key":"1051_CR21","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s10208-013-9154-z","volume":"14","author":"A Chkifa","year":"2014","unstructured":"Chkifa, A., Cohen, A., Schwab, C.: High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Found. Comput. Math. 14(4), 601\u2013633 (2014)","journal-title":"Found. Comput. Math."},{"issue":"2","key":"1051_CR22","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1016\/j.matpur.2014.04.009","volume":"103","author":"A Chkifa","year":"2015","unstructured":"Chkifa, A., Cohen, A., Schwab, C.: Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. J. Math. Pures Appl. 103(2), 400\u2013428 (2015)","journal-title":"J. Math. Pures Appl."},{"key":"1051_CR23","unstructured":"Chkifa, A., Dexter, N., Tran, H., Webster, C.G.: Polynomial approximation via compressed sensing of high-dimensional functions on lower sets. Math. Comput. 87(311), 1415\u20131450 (2018)"},{"issue":"6","key":"1051_CR24","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s10208-010-9072-2","volume":"10","author":"A Cohen","year":"2010","unstructured":"Cohen, A., DeVore, R., Schwab, C.: Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs. Found. Comput. Math. 10(6), 615\u2013646 (2010)","journal-title":"Found. Comput. Math."},{"issue":"01","key":"1051_CR25","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1142\/S0219530511001728","volume":"9","author":"A Cohen","year":"2011","unstructured":"Cohen, A., DeVore, R., Schwab, C.: Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE\u2019s. Anal. Appl. 9(01), 11\u201347 (2011)","journal-title":"Anal. Appl."},{"issue":"3","key":"1051_CR26","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/BF01890412","volume":"6","author":"C de Boor","year":"1990","unstructured":"de Boor, C., Ron, A.: On multivariate polynomial interpolation. Constr. Approx. 6(3), 287\u2013302 (1990)","journal-title":"Constr. Approx."},{"issue":"4","key":"1051_CR27","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inform. Theory 52(4), 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"1051_CR28","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1137\/0152031","volume":"52","author":"DL Donoho","year":"1992","unstructured":"Donoho, D.L., Logan, B.F.: Signal recovery and the large sieve. SIAM J. Appl. Math. 52(2), 577\u2013591 (1992)","journal-title":"SIAM J. Appl. Math."},{"issue":"8","key":"1051_CR29","doi-asserted-by":"publisher","first-page":"3015","DOI":"10.1016\/j.jcp.2011.01.002","volume":"230","author":"A Doostan","year":"2011","unstructured":"Doostan, A., Owhadi, H.: A non-adapted sparse approximation of PDEs with stochastic inputs. J. Comput. Phys. 230(8), 3015\u20133034 (2011)","journal-title":"J. Comput. Phys."},{"issue":"Supplement C","key":"1051_CR30","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.jat.2013.09.008","volume":"177","author":"N Dyn","year":"2014","unstructured":"Dyn, N., Floater, M.S.: Multivariate polynomial interpolation on lower sets. J. Approx. Theory 177(Supplement C), 34\u201342 (2014)","journal-title":"J. Approx. Theory"},{"key":"1051_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4948-7","volume-title":"A Mathematical Introduction to Compressive Sensing, Appl. Numer. Harmon. Anal.","author":"S Foucart","year":"2013","unstructured":"Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing, Appl. Numer. Harmon. Anal. Springer, New York (2013)"},{"issue":"2","key":"1051_CR32","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1109\/TIT.2011.2167214","volume":"58","author":"MP Friedlander","year":"2012","unstructured":"Friedlander, M.P., Mansour, H., Saab, R., Yilmaz, O.: Recovering compressively sampled signals using partial support information. IEEE Trans. Inform. Theory 58(2), 1122\u20131134 (2012)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1051_CR33","unstructured":"Gao, X.: Penalized methods for high-dimensional least absolute deviations regression. Ph.D. Thesis, The University of Iowa (2008)"},{"key":"1051_CR34","unstructured":"Gao, X., Huang, J.: Asymptotic analysis of high-dimensional lad regression with lasso. Stat. Sin. 20(4), 1485\u20131506 (2010)"},{"key":"1051_CR35","doi-asserted-by":"crossref","unstructured":"Grant, M., Boyd, S.: Graph implementations for nonsmooth convex programs. In: Blondel, V., Boyd, S., Kimura, H. (eds.) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, pp. 95\u2013110. Springer-Verlag Limited (2008)","DOI":"10.1007\/978-1-84800-155-8_7"},{"key":"1051_CR36","unstructured":"Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 2.1. http:\/\/cvxr.com\/cvx , March (2014)"},{"key":"1051_CR37","doi-asserted-by":"publisher","DOI":"10.1201\/b18401","volume-title":"Statistical Learning with Sparsity: the Lasso and Generalizations","author":"T Hastie","year":"2015","unstructured":"Hastie, T., Tibshirani, R., Wainwright, M.: Statistical Learning with Sparsity: the Lasso and Generalizations. CRC Press, Boca Raton (2015)"},{"issue":"3\u20134","key":"1051_CR38","first-page":"251","volume":"20","author":"F Hecht","year":"2012","unstructured":"Hecht, F.: New development in FreeFem++. J. Numer. Math. 20(3\u20134), 251\u2013265 (2012)","journal-title":"J. Numer. Math."},{"key":"1051_CR39","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.jcp.2015.02.025","volume":"289","author":"JD Jakeman","year":"2015","unstructured":"Jakeman, J.D., Eldred, M.S., Sargsyan, K.: Enhancing $$\\ell ^1$$-minimization estimates of polynomial chaos expansions using basis selection. J. Comput. Phys. 289, 18\u201334 (2015)","journal-title":"J. Comput. Phys."},{"key":"1051_CR40","doi-asserted-by":"crossref","unstructured":"Laska, J.N., Davenport, M.A., Baraniuk, R.G.: Exact signal recovery from sparsely corrupted measurements through the pursuit of justice. In: 2009 Conference Record of the 43rd Asilomar Conference on Signals, Systems and Computers, pp. 1556\u20131560. IEEE (2009)","DOI":"10.1109\/ACSSC.2009.5470141"},{"key":"1051_CR41","doi-asserted-by":"publisher","unstructured":"Li, Q., Wang, L.: Robust change point detection method via adaptive lad-lasso. Stat. Pap. 1\u201313 (2017). https:\/\/doi.org\/10.1007\/s00362-017-0927-3","DOI":"10.1007\/s00362-017-0927-3"},{"issue":"1","key":"1051_CR42","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s00365-012-9176-9","volume":"37","author":"X Li","year":"2013","unstructured":"Li, X.: Compressed sensing and matrix completion with constant proportion of corruptions. Constr. Approx. 37(1), 73\u201399 (2013)","journal-title":"Constr. Approx."},{"key":"1051_CR43","unstructured":"Logan, B.F.: Properties of high-pass signals. Ph.D. Thesis, Columbia University (1965)"},{"issue":"1","key":"1051_CR44","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/BF01893422","volume":"2","author":"GG Lorentz","year":"1986","unstructured":"Lorentz, G.G., Lorentz, R.A.: Solvability problems of bivariate interpolation I. Constr. Approx. 2(1), 153\u2013169 (1986)","journal-title":"Constr. Approx."},{"issue":"3","key":"1051_CR45","first-page":"419","volume":"14","author":"G Migliorati","year":"2014","unstructured":"Migliorati, G., Nobile, F., von Schwerin, E., Tempone, R.: Analysis of discrete $$L^2$$ projection on polynomial spaces with random evaluations. Found. Comput. Math. 14(3), 419\u2013456 (2014)","journal-title":"Found. Comput. Math."},{"issue":"4","key":"1051_CR46","doi-asserted-by":"publisher","first-page":"2017","DOI":"10.1109\/TIT.2013.2240435","volume":"59","author":"NH Nguyen","year":"2013","unstructured":"Nguyen, N.H., Tran, T.D.: Exact recoverability from dense corrupted observations via $$\\ell _1$$-minimization. IEEE Trans. Inform. Theory 59(4), 2017\u20132035 (2013)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1051_CR47","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.jcp.2014.02.024","volume":"267","author":"J Peng","year":"2014","unstructured":"Peng, J., Hampton, J., Doostan, A.: A weighted $$\\ell _1$$ minimization approach for sparse polynomial chaos expansions. J. Comput. Phys. 267, 92\u2013111 (2014)","journal-title":"J. Comput. Phys."},{"key":"1051_CR48","unstructured":"Pham, V., El\u00a0Ghaoui, L.: Robust sketching for multiple square-root lasso problems. In: Artificial Intelligence Statistics, pp. 753\u2013761 (2015)"},{"issue":"304","key":"1051_CR49","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1090\/mcom\/3113","volume":"86","author":"H Rauhut","year":"2017","unstructured":"Rauhut, H., Schwab, C.: Compressive sensing Petrov\u2013Galerkin approximation of high-dimensional parametric operator equations. Math. Comput. 86(304), 661\u2013700 (2017)","journal-title":"Math. Comput."},{"issue":"2","key":"1051_CR50","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.acha.2015.02.003","volume":"40","author":"H Rauhut","year":"2016","unstructured":"Rauhut, H., Ward, R.: Interpolation via weighted $$\\ell _1$$ minimization. Appl. Comput. Harmon. Anal. 40(2), 321\u2013351 (2016)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"1051_CR51","doi-asserted-by":"publisher","first-page":"A2492","DOI":"10.1137\/16M1059473","volume":"38","author":"Y Shin","year":"2016","unstructured":"Shin, Y., Xiu, D.: Correcting data corruption errors for multivariate function approximation. SIAM J. Sci. Comput. 38(4), A2492\u2013A2511 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"1051_CR52","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/j.sigpro.2013.07.002","volume":"94","author":"L Stankovic","year":"2014","unstructured":"Stankovic, L., Stankovic, S., Amin, M.: Missing samples analysis in signals for applications to l-estimation and compressive sensing. Signal Process. 94, 401\u2013408 (2014)","journal-title":"Signal Process."},{"key":"1051_CR53","unstructured":"Stucky, B., van\u00a0de Geer, S.A.: Sharp oracle inequalities for square root regularization (2015). arXiv:1509.04093"},{"issue":"5","key":"1051_CR54","doi-asserted-by":"publisher","first-page":"3115","DOI":"10.1109\/TIT.2011.2179701","volume":"58","author":"C Studer","year":"2012","unstructured":"Studer, C., Kuppinger, P., Pope, G., Bolcskei, H.: Recovery of sparsely corrupted signals. IEEE Trans. Inform. Theory 58(5), 3115\u20133130 (2012)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1051_CR55","unstructured":"Su, D.: Compressed sensing with corrupted Fourier measurements (2016). arXiv:1607.04926"},{"key":"1051_CR56","unstructured":"Su, D.: Data recovery from corrupted observations via l1 minimization (2016). arXiv:1601.06011"},{"issue":"4","key":"1051_CR57","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1093\/biomet\/ass043","volume":"99","author":"T Sun","year":"2012","unstructured":"Sun, T., Zhang, C.-H.: Scaled sparse linear regression. Biometrika 99(4), 879\u2013898 (2012)","journal-title":"Biometrika"},{"key":"1051_CR58","unstructured":"Tian, X., Loftus, J.R., Taylor, J.E.: Selective inference with unknown variance via the square-root lasso (2015). arXiv:1504.08031"},{"key":"1051_CR59","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Methodol. 58(1), 267\u2013288 (1996)"},{"key":"1051_CR60","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-32774-7","volume-title":"Estimation and Testing Under Sparsity","author":"SA van de Geer","year":"2016","unstructured":"van de Geer, S.A.: Estimation and Testing Under Sparsity. Springer, Berlin (2016)"},{"key":"1051_CR61","doi-asserted-by":"crossref","unstructured":"Wagener, J., Dette, H.: The adaptive lasso in high-dimensional sparse heteroscedastic models. Math. Methods Stat. 22(2), 137\u2013154 (2013)","DOI":"10.3103\/S106653071302004X"},{"issue":"3","key":"1051_CR62","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1198\/073500106000000251","volume":"25","author":"H Wang","year":"2007","unstructured":"Wang, H., Li, G., Jiang, G.: Robust regression shrinkage and consistent variable selection through the LAD-Lasso. J. Bus. Econo. Stat. 25(3), 347\u2013355 (2007)","journal-title":"J. Bus. Econo. Stat."},{"issue":"7","key":"1051_CR63","doi-asserted-by":"publisher","first-page":"3540","DOI":"10.1109\/TIT.2010.2048473","volume":"56","author":"J Wright","year":"2010","unstructured":"Wright, J., Ma, Y.: Dense error correction via $$\\ell ^1$$-minimization. IEEE Trans. Inform. Theory 56(7), 3540\u20133560 (2010)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1051_CR64","unstructured":"Xu, J.: Parameter estimation, model selection and inferences in L1-based linear regression. Ph.D. Thesis, Columbia University (2005)"},{"issue":"3","key":"1051_CR65","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s10463-008-0184-2","volume":"62","author":"J Xu","year":"2010","unstructured":"Xu, J., Ying, Z.: Simultaneous estimation and variable selection in median regression using lasso-type penalty. Ann. Inst. Stat. Math. 62(3), 487\u2013514 (2010)","journal-title":"Ann. Inst. Stat. Math."},{"issue":"3","key":"1051_CR66","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1615\/Int.J.UncertaintyQuantification.2012003925","volume":"2","author":"L Yan","year":"2012","unstructured":"Yan, L., Guo, L., Xiu, D.: Stochastic collocation algorithms using $$\\ell _1$$-minimization. Int. J. Uncertain. Quantif. 2(3), 279\u2013293 (2012)","journal-title":"Int. J. Uncertain. Quantif."},{"key":"1051_CR67","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jcp.2013.04.004","volume":"248","author":"X Yang","year":"2013","unstructured":"Yang, X., Karniadakis, G.E.: Reweighted $$\\ell ^1$$ minimization method for stochastic elliptic differential equations. J. Comput. Phys. 248, 87\u2013108 (2013)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"1051_CR68","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1109\/LSP.2013.2254712","volume":"20","author":"X Yu","year":"2013","unstructured":"Yu, X., Baek, S.J.: Sufficient conditions on stable recovery of sparse signals with partial support information. IEEE Signal Process. Lett. 20(5), 539\u2013542 (2013)","journal-title":"IEEE Signal Process. Lett."},{"issue":"476","key":"1051_CR69","doi-asserted-by":"publisher","first-page":"1418","DOI":"10.1198\/016214506000000735","volume":"101","author":"H Zou","year":"2006","unstructured":"Zou, H.: The adaptive lasso and its oracle properties. J. Am. Stat. Assoc. 101(476), 1418\u20131429 (2006)","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01051-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-019-01051-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01051-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,18]],"date-time":"2022-09-18T01:36:07Z","timestamp":1663464967000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-019-01051-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,15]]},"references-count":69,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["1051"],"URL":"https:\/\/doi.org\/10.1007\/s00211-019-01051-9","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,15]]},"assertion":[{"value":"21 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}