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Volumn 3, Issue , 2009, Pages 1360-1392

On the conditions used to prove oracle results for the lasso

Author keywords

Coherence; Compatibility; Irrepresentable condition; Lasso; Restricted eigenvalue; Restricted isometry; Sparsity

Indexed keywords


EID: 77955054299     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-EJS506     Document Type: Article
Times cited : (574)

References (24)
  • 2
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous anal-ysis of Lasso and Dantzig selector
    • Bickel, P., Ritov, Y. and Tsybakov, A. (2009). Simultaneous anal-ysis of Lasso and Dantzig selector. Annals of Statistics 37 1705-1732.
    • (2009) Annals of Statistics , vol.37 , pp. 1705-1732
    • Bickel, P.1    Ritov, Y.2    Tsybakov, A.3
  • 5
    • 38049008576 scopus 로고    scopus 로고
    • Sparse Density Estimation with ℓ1 Penalties
    • COLT, San Diego, CA, USA, June 13-15, Proceedings 530. Springer
    • Bunea, F., Tsybakov, A. and Wegkamp, M. (2007b). Sparse Density Estimation with ℓ1 Penalties. In Learning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA, June 13-15, 2007: Proceedings 530. Springer.
    • (2007) Learning Theory 20Th Annual Conference on Learning Theory
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 9
    • 69049120308 scopus 로고    scopus 로고
    • Near-ideal model selection by ℓ1 mini-mization
    • Candès, E. and Plan, Y. (2009). Near-ideal model selection by ℓ1 mini-mization. Annals of Statistics 37 2145-2177.
    • (2009) Annals of Statistics , vol.37 , pp. 2145-2177
    • Candès, E.1    Plan, Y.2
  • 11
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical esti-mation when p is much larger than n
    • Candès, E. and Tao, T. (2007). The Dantzig selector: statistical esti-mation when p is much larger than n. Annals of Statistics 35 2313-2351.
    • (2007) Annals of Statistics , vol.35 , pp. 2313-2351
    • Candès, E.1    Tao, T.2
  • 12
    • 62549157465 scopus 로고    scopus 로고
    • Sparsity in penalized empirical risk minimiza-tion. Annales de l’Institut Henri Poincaré
    • Koltchinskii, V. (2009a). Sparsity in penalized empirical risk minimiza-tion. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 45 7-57.
    • (2009) Probabilités Et Statistiques , vol.45 , pp. 7-57
    • Koltchinskii, V.1
  • 14
    • 56449113372 scopus 로고    scopus 로고
    • Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
    • Lounici, K. (2008). Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. Electronic Journal of Statistics 2 90-102.
    • (2008) Electronic Journal of Statistics , vol.2 , pp. 90-102
    • Lounici, K.1
  • 15
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the Lasso
    • Meinshausen, N. and Bühlmann, P. (2006). High-dimensional graphs and variable selection with the Lasso. Annals of Statistics 34 1436-1462.
    • (2006) Annals of Statistics , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 16
    • 65349193793 scopus 로고    scopus 로고
    • Lasso-type recovery of sparse rep-resentations for high-dimensional data
    • Meinshausen, N. and Yu, B. (2009). Lasso-type recovery of sparse rep-resentations for high-dimensional data. Annals of Statistics 37 246-270.
    • (2009) Annals of Statistics , vol.37 , pp. 246-270
    • Meinshausen, N.1    Yu, B.2
  • 17
    • 84968504291 scopus 로고
    • Extreme eigenvalues of Toeplitz forms and applications to elliptic difference equations
    • Parter, S. (1961). Extreme eigenvalues of Toeplitz forms and applications to elliptic difference equations. Transactions of the American Mathematical Society 99 153-192.
    • (1961) Transactions of the American Mathematical Society , vol.99 , pp. 153-192
    • Parter, S.1
  • 18
    • 79551473604 scopus 로고    scopus 로고
    • The deterministic Lasso
    • American Statistical Association
    • van de Geer, S. (2007). The deterministic Lasso. In JSM proceedings, (seealso http://stat.ethz.ch/research/research_reports/2007/140). American Statistical Association.
    • (2007) JSM Proceedings
    • Van De Geer, S.1
  • 19
    • 51049121146 scopus 로고    scopus 로고
    • High-dimensional generalized linear models and the Lasso
    • van de Geer, S. (2008). High-dimensional generalized linear models and the Lasso. Annals of Statistics 36 614-645.
    • (2008) Annals of Statistics , vol.36 , pp. 614-645
    • Van De Geer, S.1
  • 20
    • 65749083666 scopus 로고    scopus 로고
    • Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ1-constrained quadratic programming (Lasso)
    • Wainwright, M. (2009). Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ1-constrained quadratic programming (Lasso). IEEE Transactions on Information Theory 55 2183-2202.
    • (2009) IEEE Transactions on Information Theory , vol.55 , pp. 2183-2202
    • Wainwright, M.1
  • 21
    • 50949096321 scopus 로고    scopus 로고
    • The sparsity and bias of the Lasso selection in high-dimensional linear regression
    • Zhang, C.-H. and Huang, J. (2008). The sparsity and bias of the Lasso selection in high-dimensional linear regression. Annals of Statistics 36 1567-1594.
    • (2008) Annals of Statistics , vol.36 , pp. 1567-1594
    • Zhang, C.-H.1    Huang, J.2
  • 22
    • 69049086702 scopus 로고    scopus 로고
    • Some sharp performance bounds for least squaresregression with L1 regularization
    • Zhang, T. (2009). Some sharp performance bounds for least squaresregression with L1 regularization. Annals of Statistics 37 2109-2144.
    • (2009) Annals of Statistics , vol.37 , pp. 2109-2144
    • Zhang, T.1
  • 23


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.