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Volumn 47, Issue 1, 2011, Pages 43-74

Adaptive Dantzig density estimation

Author keywords

Calibration; Concentration inequalities; Dantzig estimate; Density estimation; Dictionary; Lasso estimate; Oracle inequalities; Sparsity

Indexed keywords


EID: 79251474881     PISSN: 02460203     EISSN: 02460203     Source Type: Journal    
DOI: 10.1214/09-AIHP351     Document Type: Article
Times cited : (30)

References (32)
  • 1
    • 61749091779 scopus 로고    scopus 로고
    • Data-driven calibration of penalties for least-squares regression
    • S. Arlot and P. Massart. Data-driven calibration of penalties for least-squares regression. J. Mach. Learn. Res. 10 (2009) 245-279.
    • (2009) J. Mach. Learn. Res. , vol.10 , pp. 245-279
    • Arlot, S.1    Massart, P.2
  • 3
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous analysis of Lasso and Dantzig selector
    • MR2533469
    • P. Bickel, Y. Ritov and A. Tsybakov. Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist. 37 (2009) 1705-1732. MR2533469
    • (2009) Ann. Statist. , vol.37 , pp. 1705-1732
    • Bickel, P.1    Ritov, Y.2    Tsybakov, A.3
  • 4
    • 77955146719 scopus 로고    scopus 로고
    • Available at arXiv 0808.1416
    • 2-loss, 2008. Available at arXiv 0808.1416.
    • (2008) 2-loss
    • Birgé, L.1
  • 5
    • 33847613502 scopus 로고    scopus 로고
    • Minimal penalties for Gaussian model selection
    • MR2288064
    • L. Birgé and P. Massart. Minimal penalties for Gaussian model selection. Probab. Theory Related. Fields 138 (2007) 33-73. MR2288064
    • (2007) Probab. Theory Related. Fields , vol.138 , pp. 33-73
    • Birgé, L.1    Massart, P.2
  • 8
    • 50849114939 scopus 로고    scopus 로고
    • Sparsity oracle inequalities for the LASSO
    • MR2312149
    • F. Bunea, A. Tsybakov and M. Wegkamp. Sparsity oracle inequalities for the LASSO. Electron. J. Statist. 1 (2007) 169-194. MR2312149
    • (2007) Electron. J. Statist. , vol.1 , pp. 169-194
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 9
    • 38049043619 scopus 로고    scopus 로고
    • Aggregation for Gaussian regression
    • MR2351101
    • F. Bunea, A. Tsybakov and M. Wegkamp. Aggregation for Gaussian regression. Ann. Statist. 35 (2007) 1674-1697. MR2351101
    • (2007) Ann. Statist. , vol.35 , pp. 1674-1697
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 10
    • 77955153854 scopus 로고    scopus 로고
    • Spades and mixture models
    • To appear. Available at arXiv 0901.2044
    • F. Bunea, A. Tsybakov, M. Wegkamp and A. Barbu. Spades and mixture models. Ann. Statist. (2010). To appear. Available at arXiv 0901.2044.
    • (2010) Ann. Statist.
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3    Barbu, A.4
  • 12
  • 13
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • MR2382644
    • E. Candès and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35 (2007) 2313-2351. MR2382644
    • (2007) Ann. Statist. , vol.35 , pp. 2313-2351
    • Candès, E.1    Tao, T.2
  • 14
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • MR1854649
    • D. Chen, D. Donoho and M. Saunders. Atomic decomposition by basis pursuit. SIAMRev. 43 (2001) 129-159. MR1854649
    • (2001) SIAMRev , vol.43 , pp. 129-159
    • Chen, D.1    Donoho, D.2    Saunders, M.3
  • 15
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • MR2237332
    • D. Donoho, M. Elad and V. Temlyakov. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 (2006) 6-18. MR2237332
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 6-18
    • Donoho, D.1    Elad, M.2    Temlyakov, V.3
  • 16
    • 0041958932 scopus 로고
    • Ideal spatial adaptation via wavelet shrinkage
    • MR1311089
    • D. Donoho and I. Johnstone. Ideal spatial adaptation via wavelet shrinkage. Biometrika 81 (1994) 425-455. MR1311089
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.1    Johnstone, I.2
  • 18
    • 33747354349 scopus 로고    scopus 로고
    • On minimax density estimation on ℝ
    • MR2046772
    • A. Juditsky and S. Lambert-Lacroix. On minimax density estimation on ℝ. Bernoulli 10 (2004) 187-220. MR2046772
    • (2004) Bernoulli , vol.10 , pp. 187-220
    • Juditsky, A.1    Lambert-Lacroix, S.2
  • 19
    • 0034287156 scopus 로고    scopus 로고
    • Asymptotics for Lasso-type estimators
    • MR1805787
    • K. Knight and W Fu. Asymptotics for Lasso-type estimators. Ann. Statist. 28 (2000) 1356-1378. MR1805787
    • (2000) Ann. Statist. , vol.28 , pp. 1356-1378
    • Knight, K.1    W Fu2
  • 20
    • 56449113372 scopus 로고    scopus 로고
    • Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
    • MR2386087
    • K. Lounici. Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. Electron. J. Stat. 2 (2008) 90-102. MR2386087
    • (2008) Electron. J. Stat. , vol.2 , pp. 90-102
    • Lounici, K.1
  • 21
    • 34247553430 scopus 로고
    • Concentration inequalities and model selection
    • Springer, Berlin. Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour July 6-23 2003
    • P. Massart. Concentration inequalities and model selection. Lecture Notes in Math. 1896. Springer, Berlin. Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour July 6-23 2003, 2007. MR2319879
    • (1896) Lecture Notes in Math.
    • Massart, P.1
  • 22
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the Lasso
    • MR2278363
    • N. Meinshausen and P. Buhlmann. High-dimensional graphs and variable selection with the Lasso. Ann. Statist. 34 (2006) 1436-1462. MR2278363
    • (2006) Ann. Statist. , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Buhlmann, P.2
  • 23
    • 65349193793 scopus 로고    scopus 로고
    • Lasso-type recovery of sparse representations for high-dimensional data
    • MR2488351
    • N. Meinshausen and B. Yu. Lasso-type recovery of sparse representations for high-dimensional data. Ann. Statist. 37 (2009) 246-270. MR2488351
    • (2009) Ann. Statist. , vol.37 , pp. 246-270
    • Meinshausen, N.1    Yu, B.2
  • 25
    • 0034215549 scopus 로고    scopus 로고
    • A new approach to variable selection in least squares problems
    • MR1773265
    • M. Osborne, B. Presnell and B. Turlach. A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20 (2000) 389-404. MR1773265
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 389-404
    • Osborne, M.1    Presnell, B.2    Turlach, B.3
  • 26
    • 77956285886 scopus 로고    scopus 로고
    • Near optimal thresholding estimation of a Poisson intensity on the real line
    • P. Reynaud-Bouret and V. Rivoirard. Near optimal thresholding estimation of a Poisson intensity on the real line. Electron. J. Statist. 4 (2010) 172-238.
    • (2010) Electron. J. Statist. , vol.4 , pp. 172-238
    • Reynaud-Bouret, P.1    Rivoirard, V.2
  • 28
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the Lasso
    • MR1379242
    • R. Tibshirani. Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. B 58 (1996) 267-288. MR1379242
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 29
    • 51049121146 scopus 로고    scopus 로고
    • High-dimensional generalized linear models and the Lasso
    • MR2396809
    • S. van de Geer. High-dimensional generalized linear models and the Lasso. Ann. Statist. 36 (2008) 614-645. MR2396809
    • (2008) Ann. Statist. , vol.36 , pp. 614-645
    • Van De Geer, S.1
  • 30
    • 33845263263 scopus 로고    scopus 로고
    • On model selection consistency of Lasso estimators
    • MR2274449
    • B. Yu and P. Zhao. On model selection consistency of Lasso estimators. J. Mach. Learn. Res. 7 (2006) 2541-2567. MR2274449
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 2541-2567
    • Yu, B.1    Zhao, P.2
  • 31
    • 50949096321 scopus 로고    scopus 로고
    • The sparsity and bias of the Lasso selection in high-dimensional linear regression
    • MR2435448
    • C. Zhang and J. Huang. The sparsity and bias of the Lasso selection in high-dimensional linear regression. Ann. Statist. 36 (2008) 1567-1594. MR2435448
    • (2008) Ann. Statist. , vol.36 , pp. 1567-1594
    • Zhang, C.1    Huang, J.2
  • 32
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive Lasso and its oracle properties
    • MR2279469
    • H. Zou. The adaptive Lasso and its oracle properties. J. Amer. Statist. Assoc. 101 (2006) 1418-1429. MR2279469
    • (2006) J. Amer. Statist. Assoc. , vol.101 , pp. 1418-1429
    • Zou, H.1


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