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Volumn 13, Issue , 2012, Pages 2107-2143

A comparison of the lasso and marginal regression

Author keywords

High dimensional regression; Lasso; Phase diagram; Regularization

Indexed keywords

COMPUTATIONAL ADVANTAGES; COVARIATES; DEPENDENT VARIABLES; HIGH PROBABILITY; HIGH-DIMENSIONAL; HIGH-DIMENSIONAL PROBLEMS; LASSO; NOISE FREE CASE; NUMBER OF DATUM; PARAMETER SPACES; RANDOM COEFFICIENTS; RATES OF CONVERGENCE; REGRESSION PROBLEM; REGULARIZATION; STATISTICAL PERFORMANCE; THEORETICAL RESULT;

EID: 84864959435     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (90)

References (31)
  • 1
    • 77952829668 scopus 로고    scopus 로고
    • Variable selection in high-dimensional linear models: Partially faithful distributions and the PC-simple algorith
    • P. Bühlmann, M. Kalisch, and M. H. Maathuis. Variable selection in high-dimensional linear models: Partially faithful distributions and the PC-simple algorith. Biometrika, 97:261-278, 2009.
    • (2009) Biometrika , vol.97 , pp. 261-278
    • Bühlmann, P.1    Kalisch, M.2    Maathuis, M.H.3
  • 2
    • 77955509952 scopus 로고    scopus 로고
    • Shifting inequality and recovery of sparse signals
    • T. Cai, L. Wang, and G. Xu. Shifting inequality and recovery of sparse signals. IEEE Transactions on Signal Processing, 59(3):1300-1308, 2010.
    • (2010) IEEE Transactions on Signal Processing , vol.59 , Issue.3 , pp. 1300-1308
    • Cai, T.1    Wang, L.2    Xu, G.3
  • 3
    • 69049120308 scopus 로고    scopus 로고
    • Near-ideal model selection by l1 minimization
    • E. J. Candès and Y. Plan. Near-ideal model selection by l1 minimization. The Annals of Statistics, 37:2145-2177, 2009.
    • (2009) The Annals of Statistics , vol.37 , pp. 2145-2177
    • Candès, E.J.1    Plan, Y.2
  • 4
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • E. J. Candés and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, 35:2313-2351, 2007.
    • (2007) The Annals of Statistics , vol.35 , pp. 2313-2351
    • Candés, E.J.1    Tao, T.2
  • 6
    • 33744552752 scopus 로고    scopus 로고
    • For most large underdetermined systems of equations, the minimal l1-norm nearsolution approximates the sparsest near-solution
    • D. Donoho. For most large underdetermined systems of equations, the minimal l1-norm nearsolution approximates the sparsest near-solution. Communications on Pure and Applied Mathematics, 59(7):907-934, 2006.
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.7 , pp. 907-934
    • Donoho, D.1
  • 7
    • 0037418225 scopus 로고    scopus 로고
    • Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization
    • DOI 10.1073/pnas.0437847100
    • D. Donoho and M. Elad. Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization. Proceedings of the National Academy of Sciences of the United States of America, 100(5):2197-2202, 2003. (Pubitemid 36297476)
    • (2003) Proceedings of the National Academy of Sciences of the United States of America , vol.100 , Issue.5 , pp. 2197-2202
    • Donoho, D.L.1    Elad, M.2
  • 8
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • DOI 10.1109/18.959265, PII S0018944801089465
    • D. Donoho and X. Huo. Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 47(7):2845-2862, 2001. (Pubitemid 33053488)
    • (2001) IEEE Transactions on Information Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 9
    • 23744475601 scopus 로고    scopus 로고
    • Higher criticism for detecting sparse heterogeneous mixtures
    • DOI 10.1214/009053604000000265
    • D. Donoho and J. Jin. Higher criticism for detecting sparse heterogeneous mixtures. The Annals of Statistics, 32(3):962-994, 2004. (Pubitemid 41250290)
    • (2004) Annals of Statistics , vol.32 , Issue.3 , pp. 962-994
    • Donoho, D.1    Jin, J.2
  • 13
    • 26844461512 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of bounded noise
    • DOI 10.1109/TIT.2005.855614
    • J.J. Fuchs. Recovery of exact sparse representations in the presence of noise. IEEE Transactions on Information Theory, 51(10):3601-3608, 2005. (Pubitemid 41448600)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.10 , pp. 3601-3608
    • Fuchs, J.J.1
  • 14
    • 84864946789 scopus 로고    scopus 로고
    • UPS delivers optimal phase diagram in high dimensional variable selection
    • P. Ji and J. Jin. UPS delivers optimal phase diagram in high dimensional variable selection. The Annals of Statistics, 40(1):73-103, 2012.
    • (2012) The Annals of Statistics , vol.40 , Issue.1 , pp. 73-103
    • Ji, P.1    Jin, J.2
  • 15
    • 42149164809 scopus 로고    scopus 로고
    • Proportion of nonzero normal means: Oracle equivalence and uniformly consistent estimators
    • J. Jin. Proportion of nonzero normal means: Oracle equivalence and uniformly consistent estimators. Journal of the Royal Statistical Society: Series B (StatisticalMethodology), 70(3):461-493, 2007.
    • (2007) Journal of the Royal Statistical Society: Series B (StatisticalMethodology , vol.70 , Issue.3 , pp. 461-493
    • Jin, J.1
  • 16
    • 0034287156 scopus 로고    scopus 로고
    • Asymptotics for lasso-type estimators
    • DOI 10.1214/aos/1015957397
    • K. Knight and W. J. Fu. Asymptotics for lasso-type estimators. The Annals of Statistics, 28:1356-1378, 2000. (Pubitemid 33244917)
    • (2000) Annals of Statistics , vol.28 , Issue.5 , pp. 1356-1378
    • Knight, K.1    Fu, W.2
  • 17
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the Lasso
    • DOI 10.1214/009053606000000281
    • N. Meinshausen and P. Bühlmann. High-dimensional graphs and variable selection with the lasso. The Annals of Statistics, 34(3):1436-1462, 2006. (Pubitemid 44231168)
    • (2006) Annals of Statistics , vol.34 , Issue.3 , pp. 1436-1462
    • Meinshausen, N.1    Buhlmann, P.2
  • 18
    • 27944433393 scopus 로고    scopus 로고
    • Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
    • DOI 10.1214/009053605000000741
    • N. Meinshausen and J. Rice. Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. The Annals of Statistics, 34(1):373-393, 2006. (Pubitemid 43836805)
    • (2006) Annals of Statistics , vol.34 , Issue.1 , pp. 373-393
    • Meinshausen, N.1    Rice, J.2
  • 20
    • 3843131653 scopus 로고    scopus 로고
    • Uniform consistency in causal inference
    • DOI 10.1093/biomet/90.3.491
    • J. M. Robins, R. Scheines, P. Spirtes, and L. Wasserman. Uniform consistency in causal inference. Biometrika, 90(3):491-515, 2003. (Pubitemid 39047137)
    • (2003) Biometrika , vol.90 , Issue.3 , pp. 491-515
    • Robins, J.M.1    Scheines, R.2    Spirtes, P.3    Wasserman, L.4
  • 25
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithic results for sparse approximation
    • J. Tropp. Greed is good: Algorithic results for sparse approximation. IEEE Transactions on Information Theory, 50(10):2231-2242, 2004.
    • (2004) IEEE Transactions on Information Theory , vol.50 , Issue.10 , pp. 2231-2242
    • Tropp, J.1
  • 26
    • 79952433487 scopus 로고    scopus 로고
    • Lecture notes Department of Mathematics University of Michigan, Available electronically via
    • R. Vershynin. Introduction to the Non-asymptotic Analysis of Random Matrices. Lecture notes, Department of Mathematics, University of Michigan, 2010. Available electronically via wwwpersonal. umich.edu/eromanv/teaching/2006- 07/280/course.html.
    • (2010) Introduction to the Non-asymptotic Analysis of Random Matrices
    • Vershynin, R.1
  • 29
    • 69049091975 scopus 로고    scopus 로고
    • High-dimensional variable selection
    • L. Wasserman and K. Roeder. High-dimensional variable selection. The Annals of Statistics, 37(5): 2178-2201, 2009.
    • (2009) The Annals of Statistics , vol.37 , Issue.5 , pp. 2178-2201
    • Wasserman, L.1    Roeder, K.2
  • 30
    • 33845263263 scopus 로고    scopus 로고
    • On model selection consistency of Lasso
    • P. Zhao and B. Yu. On model selection consistency of lasso. Journal ofMachine Learning Research, 7:2541-2563, 2006. (Pubitemid 44866738)
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 2541-2563
    • Zhao, P.1    Yu, B.2
  • 31
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive lasso and its oracle properties
    • H. Zou. The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101(476):1418-1429, 2006.
    • (2006) Journal of the American Statistical Association , vol.101 , Issue.476 , pp. 1418-1429
    • Zou, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.