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Estimating the dimension of a model. (English) Zbl 0379.62005


MSC:

62C10 Bayesian problems; characterization of Bayes procedures
62F15 Bayesian inference
62J99 Linear inference, regression
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[1] Akaike H. Information theory and an extension of the maximum likelihood principle. In: Petrov B N, Caki F, eds. Second International Symposium on Information Theory. Budapest: Akademiai Kiado, 1973. 267-281 · Zbl 0283.62006
[2] Schwarz G. Estimating the dimension of a model. Ann Statist, 1978, 6: 461-464 · Zbl 0379.62005
[3] Mallows C L. Some comments on Cp. Technometrics, 1973, 15: 661-675 · Zbl 0269.62061
[4] Tibshirani R. Regression shrinkage and selection via the Lasso. J Royal Statist Soc B, 1996, 58: 267-288 · Zbl 0850.62538
[5] Donoho D L, Huo X. Uncertainty principles and ideal atomic decomposition. IEEE Trans Inf Theory, 2001, 47: 2845-2862 · Zbl 1019.94503
[6] Donoho D L, Elad E. Maximal sparsity representation via \(l_1\) minimization. Proc Natl Acal Sci, 2003, 100: 2197-2202 · Zbl 1064.94011
[7] Chen S, Donoho D L, Saunders M. Atomic decomposition by basis pursuit. SIAM Rev, 2001, 43: 129-159 · Zbl 0979.94010
[8] Fan J, Heng P. Nonconcave penalty likelihood with a diverging number of parameters. Ann Statist, 2004, 32: 928-961 · Zbl 1092.62031
[9] Zou H. The adaptive Lasso and its oracle properties. J Amer Statist Assoc, 2006, 101: 1418-1429 · Zbl 1171.62326
[10] Zou H, Hastie T. Regularization and variable selection via the elastic net. J Royal Statist Soc B, 2005, 67: 301-320 · Zbl 1069.62054
[11] Zhao P, Yu B. Stagewise Lasso. J Mach Learn Res, 2007, 8: 2701-2726
[12] Candes E, Tao T. The Dantzig selector: Statistical estimation when \(p\) is much larger than \(n\). Ann Statist, 2007, 35: 2313-2351 · Zbl 1139.62019
[13] Knight K, Fu W J. Asymptotics for lasso-type estimators. Ann Statist, 2000, 28: 1356-1378 · Zbl 1105.62357
[14] Friedman J, Hastie T, Tibshirani R. Additive logistic regression: a statistical view of boosting. Ann Statist, 2002, 28: 337-407 · Zbl 1106.62323
[15] Efron B, Haistie T, Johnstone I, et al. Least angle regression. Ann Statist, 2004, 32: 407-499 · Zbl 1091.62054
[16] Rosset S, Zhu J. Piecewise linear regularization solution paths. Ann Statist, 2007, 35: 1012-1030 · Zbl 1194.62094
[17] Kim J, Koh K, Lustig M, et al. A method for large-scale l1-regularized least squares. IEEE J Se Top Signal Process, 2007, 1: 606-617
[18] Horst R, Thoai N V. Dc programming: preview. J Optim Th, 1999, 103: 1-41
[19] Yuille A, Rangarajan A. The concave convex procedure (CCCP). NIPS, 14. Cambridge, MA: MIT Press, 2002
[20] Candes E, Wakin M, Boyd S. Enhancing sparsity by reweighted L1 minimization. J Fourier A, 2008, 14: 877-905 · Zbl 1176.94014
[21] Blake C, Merz C. Repository of Machine Learning Databases [DB/OL]. Irvine, CA: University of California, Department of Information and Computer Science, 1998
[22] Candes E, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory, 2006, 52: 489-509 · Zbl 1231.94017
[23] Donoho D L. Compressed sensing. IEEE Trans Inf Theory, 2006, 52: 1289-1306 · Zbl 1288.94016
[24] Candes E,
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