Likelihood-based selection and sharp parameter estimation

Journal of the American Statistical Association

Volumn 107, Issue 497, 2012, Pages 223-232

  Shen, Xiaotong ^a   Pan, Wei ^a   Zhu, Yunzhang ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

(p,n) asymptotics; Continuous but nonsmooth minimization; Coordinate descent; General likelihood; Graphical models; Nonconvex

Indexed keywords

EID: 84862880599     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1080/01621459.2011.645783     Document Type: Article

References (29)

1. Banerjee, O., El Ghaoui, L., and d'Aspremont, A. (2008), "Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data," Journal of Machine Learning Research, 9, 485-516. [224]
2. Bickel, P., Ritov, Y., and Tsybakov, A. (2008), "Simultaneous Analysis of Lasso and Dantzig Selector," The Annals of Statistics, 37, 1705-1732. [228]
3. Boyd, S., and Vandenberghe, L. (2004), Convex Optimization, Cambridge UK: Cambridge University Press. [230]
4. Chen, J., and Chen, Z. (2008), "Extended Bayesian Information Criterion for Model Selection with Large Model Space," Biometrika, 95, 759-771. [224]
5. Fan, J., Feng, Y., and Wu, Y. (2009), "Network Exploration Via the Adaptive Lasso and SCAD Penalties," Annals of Applied Statistics, 3, 521-541. [230]
6. Fan, J., and Li, R. (2001), "Variable Selection Via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, 96, 1348-1360. [223,227]
7. Friedman, J., Hastie, T., and Tibshirani, R. (2008), "Sparse Inverse Covariance Estimation with the Graphical Lasso," Biostatistics, 9, 432-441. [229]
8. Gasso, G., Raotomamonjy, A., and Canu, S. (2009), "Recovering Sparse Signals with Nonconvex Penalties and DC Programming," Signal Processing, IEEE, 57, 4686-4698. [224]
9. Higgins, M. E., Claremont, M., Major, J. E., Sander, C., and Lash, A. E. (2007), "CancerGenes: A Gene Selection Resource for Cancer Genome Projects," Nucleic Acids Research, 35(suppl 1), D721-D726. [231]
10. Kim, Y., Choi, H., and Oh, H.-S. (2008), "Smoothly Clipped Absolute Deviation of High Dimensions," Journal of the American Statistical Association, 103, 1665-1673. [223]
11. Kolmogorov, A. N., and Tihomirov, V. M. (1959), "ε-entropy and ε-capacity of Sets in Function Spaces," Uspekhi Matematicheskikh Nauk, 14, 3-86. [In Russian. English translation, American Mathematical Society, 2, 17, 277-364. (1961).] [226]
12. Li, H., and Gui, J. (2006), "Gradient Directed Regularization for Sparse Gaussian Concentration Graphs, with Applications to Inference of Genetic Networks," Biostatistics, 7, 302-317. [224]
13. Meinshausen, N., and Buhlmann, P. (2006), "High Dimensional Graphs and Variable Selection with the Lasso," The Annals of Statistics, 34, 1436-1462. [223,224]
14. Negahban, S., Wainwright, M., Ravikumar, P., and Yu, B. (2010), "A Unified Framework for High-Dimensional Analysis of M-estimators with Decomposable Regularizers," Technical Report, Department of Statistics, University of California, Berkley. [223]
15. Raskutti, G.,Wainwright,M., and Yu, B. (2009), "Minimax Rates of Estimation for High-Dimensional Linear Regression over lq Balls," University California, Berkeley: Tech Report. [224,226]
16. Rocha, G., Zhao, P., and Yu, B. (2008), "A Path Following Algorithm for Sparse Pseudo-Likelihood Inverse Covariance Estimation," Technical Report 759, University of California, Berkeley. [224]
17. Rothman, A., Bickel, P., Levina, E., and Zhu, J. (2008), "Sparse Permutation Invariant Covariance Estimation," Electronic Journal of Statistics, 2, 494-515. [224]
18. Rothman, A., Bickel, P., Levina, E., and Zhu, J. (2009), "A New Approach to Cholesky-based Covariance Regularization in High Dimensions," Biometrika, 97, 539-550. [224,230]
19. Schwarz, G. (1978), "Estimating the Dimension of a Model," The Annals of Statistics, 6, 461-64. [223]
20. Shen, X., and Ye, J. (2002), "Adaptive Model Selection," Journal of the American Statistical Association, 97, 210-221. [224]
21. Shen, X., Pan, W., Zhu, Y., and Zhou, H. (2010), "On Constrained and Regularization for High-Dimensional Regression," Technical Report, Division of Biostatistics, University of Minnesota. [225]
22. Tibshirani, R. (1996), "Regression Shrinkage and Selection Via the LASSO," Journal of the Royal Statistical Society, Series B, 58, 267-288. [223]
23. Wang, Y., Klijn, J. G., E-Wang, Y., Klijn, J. G., Zhang, Y., Sieuwerts, A., Look, M., Yang, F., Talantov, D., Timmermans, M., Meijer-van Gelder, M., Yu, J., Jatkoe, T., Berns, E., Atkins, D., and Foekens, J. (2005), "Gene-Expression Profiles to Predict Distant Metastasis of Lymph-Node-Negative Primary Breast Cancer," Lancet, 365, 671-679. [230]
24. Wei, Z., and Li, H. (2007), "Nonparametric Pathway-based Regression Models for Analysis of Genomic Data," Biostatistics, 8, 265-284. [230]
25. Yuan, M., and Lin, Y. (2007), "Model Selection and Estimation in the Gaussian Graphical Model," Biometrika, 94, 19-35. [224]
26. Zhang, C.-H. (2010), "Nearly Unbiased Variable Selection Under Minimax Concave Penalty," The Annals of Statistics, 38, 894-942. [228]
27. Zou, H., and Li, R. (2008), "One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models" (with discussion), Annals of Statistics, 36, 1509-1566. [227]
28. Zhao, P., andYu, B. (2006), "On Model Selection Consistency of Lasso," Journal of Machine Learning Research, 7, 2541-2563. [223]
29. Zhou, S. (2010), "Thresholded Lasso for High-Dimensional Variable Selection and Statistical Estimation, Technical Report, Department of Statistics, University of Michigan. [228]