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Volumn 37, Issue 6 B, 2009, Pages 3779-3821

High-dimensional additive modeling

Author keywords

Group lasso; Model selection; Nonparametric regression; Oracle inequality; Penalized likelihood; Sparsity

Indexed keywords


EID: 73949083829     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS692     Document Type: Article
Times cited : (365)

References (34)
  • 1
    • 73949151477 scopus 로고    scopus 로고
    • AGMON, S. (1965). Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton, NJ. MR0178246
    • AGMON, S. (1965). Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton, NJ. MR0178246
  • 2
    • 0036997840 scopus 로고    scopus 로고
    • BARAUD, Y. (2002). Model selection for regression on a random design. ESAIM Probab. Stat. 6 127-146. MR1918295
    • BARAUD, Y. (2002). Model selection for regression on a random design. ESAIM Probab. Stat. 6 127-146. MR1918295
  • 3
    • 68649086910 scopus 로고    scopus 로고
    • BICKEL, P., RITOV, Y. and TSYBAKOV, A. (2009). Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 1705-1732. MR1056344
    • BICKEL, P., RITOV, Y. and TSYBAKOV, A. (2009). Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 1705-1732. MR1056344
  • 4
    • 0037561860 scopus 로고    scopus 로고
    • A Bennet concentration inequality and its application to suprema of empirical processes
    • MR1890640
    • BOUSQUET, O. (2002). A Bennet concentration inequality and its application to suprema of empirical processes. C. R. Math. Acad. Sci. Paris 334 495-550. MR1890640
    • (2002) C. R. Math. Acad. Sci. Paris , vol.334 , pp. 495-550
    • BOUSQUET, O.1
  • 5
    • 41549141939 scopus 로고    scopus 로고
    • Boosting algorithms: Regularization, prediction and model fitting
    • BÜHLMANN, P. and HOTHORN, T. (2007). Boosting algorithms: Regularization, prediction and model fitting. Statist. Sci. 22 477-505.
    • (2007) Statist. Sci , vol.22 , pp. 477-505
    • BÜHLMANN, P.1    HOTHORN, T.2
  • 6
    • 73949158752 scopus 로고    scopus 로고
    • Variable selection for highdimensional models: Partially faithful distributions and the PC-simple algorithm
    • Technical report, ETH Zürich
    • BÜHLMANN, P., KALISCH, M. and MAATHUIS, M. (2009). Variable selection for highdimensional models: Partially faithful distributions and the PC-simple algorithm. Technical report, ETH Zürich.
    • (2009)
    • BÜHLMANN, P.1    KALISCH, M.2    MAATHUIS, M.3
  • 7
    • 0043245810 scopus 로고    scopus 로고
    • Boosting with the L2 loss: Regression and classification
    • MR1995709
    • BÜHLMANN, P. and YU, B. (2003). Boosting with the L2 loss: Regression and classification. J. Amer. Statist. Assoc. 98 324-339. MR1995709
    • (2003) J. Amer. Statist. Assoc , vol.98 , pp. 324-339
    • BÜHLMANN, P.1    YU, B.2
  • 8
    • 33746056860 scopus 로고    scopus 로고
    • 1- penalized least squares. In Learning Theory. Lecture Notes in Computer Science 4005 379-391. Springer, Berlin. MR2280619
    • 1- penalized least squares. In Learning Theory. Lecture Notes in Computer Science 4005 379-391. Springer, Berlin. MR2280619
  • 9
    • 50849114939 scopus 로고    scopus 로고
    • Sparsity oracle inequalities for the lasso
    • MR2312149
    • BUNEA, F., TSYBAKOV, A. and WEGKAMP, M. H. (2007). Sparsity oracle inequalities for the lasso. Electron. J. Stat. 1 169-194. MR2312149
    • (2007) Electron. J. Stat , vol.1 , pp. 169-194
    • BUNEA, F.1    TSYBAKOV, A.2    WEGKAMP, M.H.3
  • 10
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • MR2382644
    • CANDES, E. and TAO, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35 2313-2351. MR2382644
    • (2007) Ann. Statist , vol.35 , pp. 2313-2351
    • CANDES, E.1    TAO, T.2
  • 11
    • 0037453009 scopus 로고    scopus 로고
    • Integrating regulatory motif discovery and genome-wide expression analysis
    • CONLON, E. M., LIU, X. S., LIEB, J. D. and LIU, J. S. (2003). Integrating regulatory motif discovery and genome-wide expression analysis. Proc. Nat. Acad. Sci. U. S. A. 100 3339-3344.
    • (2003) Proc. Nat. Acad. Sci. U. S. A , vol.100 , pp. 3339-3344
    • CONLON, E.M.1    LIU, X.S.2    LIEB, J.D.3    LIU, J.S.4
  • 12
    • 53849086824 scopus 로고    scopus 로고
    • Sure independence screening for ultra-high-dimensional feature space
    • FAN, J. and LV, J. (2008). Sure independence screening for ultra-high-dimensional feature space. J. R. Stat. Soc. Ser. B Stat. Methodol. 70 849-911.
    • (2008) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.70 , pp. 849-911
    • FAN, J.1    LV, J.2
  • 13
    • 73949141480 scopus 로고    scopus 로고
    • GREEN, P. J. and SILVERMAN, B. W. (1994). Nonparametric Regression and Generalized Linear Models. Monographs on Statistics and Applied Probability 58. Chapman and Hall, London. MR1270012
    • GREEN, P. J. and SILVERMAN, B. W. (1994). Nonparametric Regression and Generalized Linear Models. Monographs on Statistics and Applied Probability 58. Chapman and Hall, London. MR1270012
  • 14
    • 31344454903 scopus 로고    scopus 로고
    • Persistency in high-dimensional linear predictorselection and the virtue of over-parametrization
    • MR2108039
    • GREENSHTEIN, E. and RITOV, Y. (2004). Persistency in high-dimensional linear predictorselection and the virtue of over-parametrization. Bernoulli 10 971-988. MR2108039
    • (2004) Bernoulli , vol.10 , pp. 971-988
    • GREENSHTEIN, E.1    RITOV, Y.2
  • 15
    • 73949131041 scopus 로고    scopus 로고
    • HÄRDLE, W., MÜLLER, M., SPERLICH, S. and WERWATZ, A. (2004). Nonparametric and Semiparametric Models. Springer, New York. MR2061786
    • HÄRDLE, W., MÜLLER, M., SPERLICH, S. and WERWATZ, A. (2004). Nonparametric and Semiparametric Models. Springer, New York. MR2061786
  • 16
    • 33746126624 scopus 로고    scopus 로고
    • BLOCKWISE sparse regression
    • MR2267240
    • KIM, Y, KIM, J. and KIM, Y (2006). BLOCKWISE sparse regression. STATIST. SINICA 16 375-390. MR2267240
    • (2006) STATIST. SINICA , vol.16 , pp. 375-390
    • KIM, Y.1    KIM, J.2    KIM, Y.3
  • 17
    • 84860650487 scopus 로고    scopus 로고
    • Sparse recovery in large ensembles of kernel machines
    • R. A. Servedio and T. Zhang, eds, Omnipress, Madison, WI
    • KOLTCHINSKII, V. and YUAN, M. (2008). Sparse recovery in large ensembles of kernel machines. In COLT (R. A. Servedio and T. Zhang, eds.) 229-238. Omnipress, Madison, WI.
    • (2008) COLT , pp. 229-238
    • KOLTCHINSKII, V.1    YUAN, M.2
  • 18
    • 73949119868 scopus 로고    scopus 로고
    • LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin. MR1102015
    • LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin. MR1102015
  • 19
    • 33847350805 scopus 로고    scopus 로고
    • Component selection and smoothing in multivariate nonparametric regression
    • MR2291500
    • LIN, Y. and ZHANG, H. H. (2006). Component selection and smoothing in multivariate nonparametric regression. Ann. Statist. 34 2272-2297. MR2291500
    • (2006) Ann. Statist , vol.34 , pp. 2272-2297
    • LIN, Y.1    ZHANG, H.H.2
  • 20
    • 0036324753 scopus 로고    scopus 로고
    • An algorithm for finding protein-DNA binding sites with applications to chromatin-immunoprecipitation microarray experiments
    • LIU, X. S., BRUTLAG, D. L. and LIU, J. S. (2002). An algorithm for finding protein-DNA binding sites with applications to chromatin-immunoprecipitation microarray experiments. Nature Biotechnology 20 835-839.
    • (2002) Nature Biotechnology , vol.20 , pp. 835-839
    • LIU, X.S.1    BRUTLAG, D.L.2    LIU, J.S.3
  • 23
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the lasso
    • MR2278363
    • MEINSHAUSEN, N. and BÜHLMANN, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436-1462. MR2278363
    • (2006) Ann. Statist , vol.34 , pp. 1436-1462
    • MEINSHAUSEN, N.1    BÜHLMANN, P.2
  • 24
    • 65349193793 scopus 로고    scopus 로고
    • Lasso-type recovery of sparse representations for highdimensional data
    • MR2488351
    • MEINSHAUSEN, N. and YU, B. (2009). Lasso-type recovery of sparse representations for highdimensional data. Ann. Statist. 37 246-270. MR2488351
    • (2009) Ann. Statist , vol.37 , pp. 246-270
    • MEINSHAUSEN, N.1    YU, B.2
  • 27
    • 3042574880 scopus 로고    scopus 로고
    • Amlet, Ramlet, and Gamlet: Automatic nonlinear fitting of additive models, robust and generalized, with wavelets
    • MR2063986
    • SARDY, S. and TSENG, P. (2004). Amlet, Ramlet, and Gamlet: Automatic nonlinear fitting of additive models, robust and generalized, with wavelets. J. Comput. Graph. Statist. 13 283-309. MR2063986
    • (2004) J. Comput. Graph. Statist , vol.13 , pp. 283-309
    • SARDY, S.1    TSENG, P.2
  • 28
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • MR1379242
    • TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267-288. MR1379242
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , pp. 267-288
    • TIBSHIRANI, R.1
  • 30
    • 51049121146 scopus 로고    scopus 로고
    • HIGH-dimensional generalized linear models and the lasso
    • MR2396809
    • VAN DE GEER, S. (2008). HIGH-dimensional generalized linear models and the lasso. ANN. STATIST. 36 614-645. MR2396809
    • (2008) ANN. STATIST , vol.36 , pp. 614-645
    • VAN DE GEER, S.1
  • 31
    • 73949125183 scopus 로고    scopus 로고
    • VAN DER VAART, A. and WELLNER, J. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671
    • VAN DER VAART, A. and WELLNER, J. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671
  • 32
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • MR2212574
    • YUAN, M. and LIN, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 49-67. MR2212574
    • (2006) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.68 , pp. 49-67
    • YUAN, M.1    LIN, Y.2
  • 33
    • 50949096321 scopus 로고    scopus 로고
    • The sparsity and bias of the lasso selection in highdimensional linear regression
    • MR2435448
    • ZHANG, C.-H. and HUANG, J. (2008). The sparsity and bias of the lasso selection in highdimensional linear regression. Ann. Statist. 36 1567-1594. MR2435448
    • (2008) Ann. Statist , vol.36 , pp. 1567-1594
    • ZHANG, C.-H.1    HUANG, J.2
  • 34
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive lasso and its oracle properties
    • MR2279469
    • ZOU, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418-1429. MR2279469
    • (2006) J. Amer. Statist. Assoc , vol.101 , pp. 1418-1429
    • ZOU, H.1


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