SEARCH

SEARCH BY CITATION

References

  • Antoniadis, A. and Fan, J. (2001) Regularization of wavelets approximations (with discussion). J. Am. Statist. Ass., 96, 939967.
  • Bai, Z. D. (1999) Methodologies in spectral analysis of large dimensional random matrices, a review. Statist. Sin., 9, 611677.
  • Bai, Z. D. and Yin, Y. Q. (1993) Limit of smallest eigenvalue of a large dimensional sample covariance matrix. Ann. Probab., 21, 12751294.
  • Baron, D., Wakin, M. B., Duarte, M. F., Sarvotham, S. and Baraniuk, R. G. (2005) Distributed compressed sensing. Manuscript.
  • Barron, A., Cohen, A., Dahmen, W. and DeVore, R. (2008) Approximation and learning by greedy algorithms. Ann. Statist., 36, 6494.
  • Bickel, P. J. and Levina, E. (2004) Some theory for Fisher's linear discriminant function, ‘‘naive Bayes’’, and some alternatives when there are many more variables than observations. Bernoulli, 10, 9891010.
  • Bickel, P. J. and Levina, E. (2008) Regularized estimation of large covariance matrices. Ann. Statist., 36, 199227.
  • Bickel, P. J., Ritov, Y. and Tsybakov, A. (2008) Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist., 36, in the press.
  • Breiman, L. (1995) Better subset regression using the nonnegative garrote. Technometrics, 37, 373384.
  • Breiman, L. (1996) Heuristics of instability and stabilization in model selection. Ann. Statist., 24, 23502383.
  • Candes, E. and Tao, T. (2007) The Dantzig selector: statistical estimation when p is much larger than n (with discussion). Ann. Statist., 35, 23132404.
  • Chikuse, Y. (2003) Statistics on special manifolds. Lect. Notes Statist, 174.
  • Donoho, D. L. (2000) High-dimensional data analysis: the curses and blessings of dimensionality. American Mathematical Society Conf. Math Challenges of the 21st Century.
  • Donoho, D. L. and Elad, M. (2003) Maximal sparsity representation via l1 minimization. Proc. Natn. Acad. Sci. USA, 100, 21972202.
  • Donoho, D. L. and Huo, X. (2001) Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory, 47, 28452862.
  • Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425455.
  • Eaton, M. L. (1989) Group Invariance Applications in Statistics. Hayward: Institute of Mathematical Statistics.
  • Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004) Least angle regression (with discussion). Ann. Statist., 32, 407499.
  • Fan, J. (1997) Comments on ‘‘Wavelets in statistics: a review,’’ by A. Antoniadis. J. Ital. Statist. Ass., 6, 131138.
  • Fan, J. and Fan, Y. (2008) High dimensional classification using features annealed independence rules. Ann. Statist., to be published.
  • Fan, J. and Li, R. (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Statist. Ass., 96, 13481360.
  • Fan, J. and Li, R. (2002) Variable selection for Cox's proportional hazards model and frailty model. Ann. Statist., 30, 7499.
  • Fan, J. and Li, R. (2006) Statistical challenges with high dimensionality: feature selection in knowledge discovery. In Proc. Int. Congr. Mathematicians (eds M.Sanz-Sole, J.Soria, J. L.Varona and J.Verdera), vol. III, pp. 595622. Freiburg: European Mathematical Society.
  • Fan, J. and Peng, H. (2004) Nonconcave penalized likelihood with diverging number of parameters. Ann. Statist., 32, 928961.
  • Fan, J. and Ren, Y. (2006) Statistical analysis of DNA microarray data. Clin. Cancer Res., 12, 44694473.
  • Frank, I. E. and Friedman, J. H. (1993) A statistical view of some chemometrics regression tools (with discussion). Technometrics, 35, 109148.
  • Freund, Y. and Schapire, R. E. (1997) A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci., 55, 119139.
  • Friedman, J., Hastie, T., Höfling, H. and Tibshirani, R. (2007) Pathwise coordinate optimization. Ann. Appl. Statist., 1, 302332.
  • Geman, S. (1980) A limit theorem for the norm of random matrices. Ann. Probab., 8, 252261.
  • George, E. I. and McCulloch, R. E. (1997) Approaches for Bayesian variable selection. Statist. Sin., 7, 339373.
  • Golub, T. R., Slonim, D. K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J. P., Coller, H., Loh, M. L., Downing, J. R., Caligiuri, M. A., Bloomfield, C. D. and Lander, E. S. (1999) Molecular classification of cancer: class discovery and class prediction by expression monitoring. Science, 286, 531537.
  • Greenshtein, E. (2006) Best subset selection, persistence in high dimensional statistical learning and optimization under l1 constraint. Ann. Statist., 34, 23672386.
  • Greenshtein, E. and Ritov, Y. (2004) Persistence in high-dimensional linear predictor selection and the virtue of overparametrization. Bernoulli, 10, 971988.
  • Grenander, U. and Szegö, G. (1984) Toeplitz Forms and Their Applications. New York: Chelsea.
  • Gribonval, R., Mailhe, B., Rauhut, H., Schnass, K. and Vandergheynst, P. (2007) Average case analysis of multichannel thresholding. In Proc. Int. Conf. Acoustic and Speech Signal Processing. New York: Institute of Electrical and Electronics Engineers.
  • Hall, P., Marron, J. S. and Neeman, A. (2005) Geometric representation of high dimension, low sample size data. J. R. Statist. Soc. B, 67, 427444.
  • Huang, J., Horowitz, J. and Ma, S. (2008) Asymptotic properties of bridge estimators in sparse high-dimensional regression models. Ann. Statist., 36, 587613.
  • Hunter, D. and Li, R. (2005) Variable selection using MM algorithms. Ann. Statist., 33, 16171642.
  • Johnstone, I. M. (2001) On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist., 29, 295327.
  • Knight, K. and Fu, W. (2000) Asymptotics for Lasso-type estimators. Ann. Statist., 28, 13561378.
  • Lam, C. and Fan, J. (2007) Sparsistency and rates of convergence in large covariance matrices estimation. Manuscript.
  • Ledoux, M. (2001) The Concentration of Measure Phenomenon. Cambridge: American Mathematical Society.
  • Ledoux, M. (2005) Deviation inequalities on largest eigenvalues. Manuscript.
  • Meier, L., Van De Geer, S. and Bühlmann, P. (2008) The group lasso for logistic regression. J. R. Statist. Soc. B, 70, 53-71.
  • Meinshausen, N. (2007) Relaxed Lasso. Computnl Statist. Data Anal., 52, 374393.
  • Meinshausen, N. and Bühlmann, P. (2006) High dimensional graphs and variable selection with the Lasso. Ann. Statist., 34, 14361462.
  • Meinshausen, N., Rocha, G. and Yu, B. (2007) Discussion of ‘‘The Dantzig selector: statistical estimation when p is much larger than n’’. Ann. Statist., 35, 23732384.
  • Nikolova, M. (2000) Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math., 61, 633658.
  • Paul, D., Bair, E., Hastie, T. and Tibshirani, R. (2008) ‘‘Pre-conditioning’’ for feature selection and regression in high-dimensional problems. Ann. Statist., to be published.
  • Ravikumar, P., Lafferty, J., Liu, H. and Wasserman, L. (2007) Sparse additive models. Manuscript.
  • Silverstein, J. W. (1985) The smallest eigenvalue of a large dimensional Wishart matrix. Ann. Probab., 13, 13641368.
  • Storey, J. D. and Tibshirani, R. (2003) Statistical significance for genome-wide studies. Proc. Natn. Acad. Sci. USA, 100, 94409445.
  • Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267288.
  • Tibshirani, R., Hastie, T., Narasimhan, B. and Chu, G. (2002) Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proc. Natn. Acad. Sci. USA, 99, 65676572.
  • Van Der Vaart, A. W. and Wellner, J. A. (1996) Weak Convergence and Empirical Processes. New York: Springer.
  • Zhang, C.-H. (2007) Penalized linear unbiased selection. Technical Report 2007-003. Department of Statistics, Rutgers University, Piscataway.
  • Zhang, C.-H. and Huang, J. (2008) The sparsity and bias of the LASSO selection in high-dimensional linear regression. Ann. Statist., 36, 15671594.
  • Zhao, P. and Yu, B. (2006) On model selection consistency of Lasso. J. Mach. Learn. Res., 7, 25412567.
  • Zou, H. (2006) The adaptive Lasso and its oracle properties. J. Am. Statist. Ass., 101, 14181429.
  • Zou, H. and Li, R. (2008) One-step sparse estimates in nonconcave penalized likelihood models. Ann. Statist., to be published.