Model selection via adaptive shrinkage with t priors

Computational Statistics

Volumn 25, Issue 3, 2010, Pages 441-461

  Armagan, Artin ^a   Zaretzki, Russell L ^b  

^a Duke University   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Elastic net; Lasso; Regularized least squares; Relevance vector machine; Ridge regression; Shrinkage estimation

Indexed keywords

EID: 77954542756     PISSN: 09434062     EISSN: 16139658     Source Type: Journal    
DOI: 10.1007/s00180-010-0186-4     Document Type: Article

References (31)

1. Angers JF, Berger JO (1991) Robust hierarchical bayes estimation of exchangeable means. Can J Stat 19: 39-56.
2. Bae K, Mallick BK (2004) Gene selection using a two-level hierarchical Bayesian model. Bioinformatics 20(18): 3423-3430.
3. Breiman L (1995) Better subset regression using the nonnegative garrote. Technometrics 37(4): 373-384.
4. Breiman L, Friedman JH (1985) Estimating optimal transformations for multiple regression and correlation. J Am Stat Assoc 80(391): 580-598.
5. Brown P, Vannucci M, Fearn T (1998) Multivariable bayesian variable selection and prediction. J R Stat Soc Series B 60(3): 627-641.
6. Candes E, Tao T (2007) The dantzig selector: statistical estimation when p is much larger than n. Ann Stat 35(6): 2313-2351.
7. Casella G, Moreno E (2006) Objective bayesian variable selection. J Am Stat Assoc 101(473): 157-167.
8. Chen MH, Shao QM, Ibrahim JG (2001) Monte Carlo methods in Bayesian computation. Springer, Berlin.
9. Chipman H, George EI, McCulloch RE (2001) The practical implementation of bayesian model selection. IMS Lecture notes-monograph series, vol 38, pp 65-116.
10. Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2): 407-499.
11. Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96: 1348-1360.
12. Figueiredo MAT (2003) Adaptive sparseness for supervised learning. IEEE Trans Pattern Anal Mach Intell 25: 1150-1159.
13. George EI (2000) The variable selection problem. J Am Stat Assoc 95: 1304-1308.
14. Geweke J (1993) Bayesian treatment of the independent student-t linear model. J Appl Econom 8(S): S19-40.
15. Griffen JE, Brown PJ (2007) Bayesian adaptive lassos with non-convex penalization. Technical Report 07-2v2, Centre for Research in Statistical Methodology. University of Warwick, UK.
16. Harville DA (1977) Maximum likelihood approaches to variance component estimation and to related problems. J Am Stat Assoc 72(358): 320-338.
17. Hoerl AE, Kennard RW (2000) Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 42(1): 80-86.
18. Johnstone IM, Silverman BW (2005) Empirical bayes selection of wavelet thresholds. Ann Stat 33: 1700-1752.
19. Kiiveri H (2003) A bayesian approach to variable selection when the number of variables is very large. IMS Lecture Notes - Monograph Series 40: 127-143.
20. Lindley DV, Smith AFM (1972) Bayes estimates for the linear model. J R Stat Soc Series B 34(1): 1-41.
21. O'Hagan A (1976) On posterior joint and marginal modes. Biometrika 63(2): 329-333.
22. Park T, Casella G (2008) The bayesian lasso. J Am Stat Assoc 103: 681-686.
23. Smith M, Kohn R (1996) Nonparametric regression using Bayesian variable selection. J Econom 75(2): 317-343.
24. Sorensen D, Gianola D (2002) Likelihood, Bayesian, and MCMC methods in quantitative genetics. Springer, New York.
25. Sun L, Hsu JSJ, Guttman I, Leonard T (1996) Bayesian methods for variance component models. J Am Stat Assoc 91(434): 743-752.
26. ter Braak CJ (2005) Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising. Comput Stat Data Anal 51(2): 1232-1242.
27. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Series B 58(1): 267-288.
28. Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1: 211-244.
29. Yuan M, Lin Y (2005) Efficient empirical Bayes variable selection and estimation in linear models. J Am Stat Assoc 100(472): 1215-1225.
30. Zhao P, Yu B (2006) On model selection consistency of lasso. J Mach Learn Res 7: 2541-2563.
31. Zou H (2006) The adaptive lasso and its oracle properties. J Am Stat Assoc 101: 1418-1429.