Consistent high-dimensional Bayesian variable selection via penalized credible regions

Journal of the American Statistical Association

Volumn 107, Issue 500, 2012, Pages 1610-1624

  Bondell, Howard D ^a   Reich, Brian J ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Consistency; Credible region; LASSO; Stochastic search

Indexed keywords

EID: 84871951819     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2012.716344     Document Type: Article

References (38)

1. Barbieri, M., and Berger, J. O. (2004), "Optimal Predictive Model Selection," The Annals of Statistics, 32, 870-897.
2. Bondell, H. D., and Reich, B. J. (2008), "Simultaneous Regression Shrinkage, Variable Selection and Clustering of Predictors With OSCAR," Biometrics, 64, 115-123.
3. Breiman, L. (1995), "Better Subset Regression Using the Nonnegative Garrote," Technometrics, 37, 373-384.
4. Brown, P. J., Vannucci, M., and Fearn, T. (2002), "Bayes Model Averaging With Selection of Regressors," Journal of the Royal Statistical Society, Series B, 64, 519-536.
5. Candes, E., and Tao, T. (2007), "The Dantzig Selector: Statistical Estimation When p is Much Larger Than n" (with discussion), The Annals of Statistics, 35, 2313-2351.
6. Carlin, B. P., and Louis, T. A. (2009), Bayesian Methods for Data Analysis, New York: CRC Press.
7. Davis, J., and Goadrich, M. (2006), "The Relationship Between Precision-Recall and ROC Curves," in Proceedings of the 23rd International Conference on Machine Learning, pp. 233-240.
8. Dunson, D. B., Herring, A. H., and Engel, S. M. (2008), "Bayesian Selection and Clustering of Polymorphisms in Functionally-Related Genes," Journal of the American Statistical Association, 103, 534-546.
9. Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), "Least Angle Regression," The Annals of Statistics, 32, 407-499.
10. 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.
11. Fan, J., and Lv, J. (2008), "Sure Independence Screening for Ultra-High Dimensional Feature Space"(withdiscussion), Journal of the Royal Statistical Society, Series B, 70, 849-911.
12. George, E. I., and Foster, D. P. (2000), "Calibration and Empirical Bayes Variable Selection," Biometrika, 87, 731-747.
13. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling," Journal of the American Statistical Association, 88, 881-889.
14. George, E. I., and McCulloch, R. E. (1997), "Approaches for Bayesian Variable Selection," Statistica Sinica, 7, 339-373.
15. Huang, J., Horowitz, J. L., and Ma, S. G. (2008), "Asymptotic Properties of Bridge Estimators in Sparse High-Dimensional Regression Models," The Annals of Statistics, 36, 587-613.
16. Huang, J., Ma, S. G., and Zhang, C. -H. (2008), "Adaptive Lasso for Sparse High-Dimensional Regression Models," Statistica Sinica, 18, 1603-1618.
17. James, G. M., Radchenko, P., and Lv, J. (2009), "DASSO: Connections Between the Dantzig Selector and Lasso," Journal of the Royal Statistical Society, Series B, 71, 127-142.
18. Jung, S., and Marron, J. S. (2009), "PCA Consistency in High Dimension, Low Sample Size Context," The Annals of Statistics, 37, 4104-4130.
19. Kinney, S., and Dunson, D. B. (2007), "Fixed and Random Effects Selection in Linear and Logistic Models," Biometrics, 63, 690-698.
20. Lan, H., Chen, M., Flowers, J. B., Yandell, B. S., Stapleton, D. S., Mata, C. M., Mui, E. T., Flowers, M. T., Schueler, K. L., Manly, K. F., Williams, R. W., Kendziorski, K., and Attie, A. D. (2006), "Combined Expression Trait Correlationsand Expression Quantitative Trait LocusMapping," PLoS Genetics, 2, e6.
21. Liang, F., Paulo, R., Molina, G., Clyde, M., and Berger, J. O. (2008), "Mixtures of g-Priors for Bayesian Variable Selection," Journal of the American Statistical Association, 103, 410-423.
22. Lv, J., and Fan, Y. (2009), "A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares," The Annals of Statistics, 37, 3498-3528.
23. Meinshausen, N., and Buhlmann, P. (2006), "High Dimensional Graphs and Variable Selection With the Lasso,"The Annals of Statistics, 34, 1436-1462.
24. Moreno, E., Girón, F. J., and Casella, G. (2010), "Consistency of Objective Bayes Factors as the Model Dimension Grows," The Annals of Statistics, 38, 1937-1952.
25. O'Hara, R. B., and Sillanpää, M. J. (2009), "A Review of Bayesian Variable Selection Methods: What, How and Which," Bayesian Analysis, 4, 85-118.
26. Scott, J. G., and Berger, J. O. (2010), "Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem," The Annals of Statistics, 38, 2587-2619.
27. Tadesse, M. G., Sha, N., and Vannucci, M. (2005), "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, 100, 602-617.
28. Tibshirani, R. (1996), "Regression Shrinkage and Selection via the Lasso," Journal of the Royal Statistical Society, Series B, 58, 267-288.
29. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005), "Sparsity and Smoothness via the Fused Lasso," Journal of the Royal Statistical Society, Series B, 67, 91-108.
30. Wang, H. (2009), "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, 104, 1512-1524.
31. Yata, K., and Aoshima, M. (2009), "PCA Consistency for Non-Gaussian Data in High Dimension, Low Sample Size Context," Communications in Statistics-Theory and Methods, 38, 2634-2652.
32. Yuan, M., and Lin, Y. (2006), "Model Selection and Estimation in Regression With Grouped Variables," Journal of the Royal Statistical Society, Series B, 68, 49-67.
33. Zellner, A. (1986), "On Assessing Prior Distributions and Bayesian Regression Analysis With g-Prior Distributions," in Bayesian Inference and Decision Techniques: Essays in Honour of Bruno de Finetti, eds. P. K. Goel and A. Zellner, Amsterdam: North-Holland, pp. 233-243.
34. Zhang, D., Lin, Y., and Zhang, M. (2009), "Penalized Orthogonal-Components Regression for Large p Small n Data," Electronic Journal of Statistics, 3, 781-796.
35. Zhao, P., and Yu, B. (2006), "On Model Selection Consistency of Lasso," Journal of Machine Learning Research, 7, 2541-2563.
36. Zou, H. (2006), "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, 101, 1418-1429.
37. Zou, H., and Hastie, T. (2005), "Regularization and Variable Selection via the Elastic Net," Journal of the Royal Statistical Society, Series B, 67, 301-320.
38. Zou, H., and Li, R. (2008), "One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models" (with discussion), The Annals of Statistics, 36, 1509-1566.