Estimation, prediction and inference for the LASSO random effects model

Australian and New Zealand Journal of Statistics

Volumn 51, Issue 1, 2009, Pages 43-61

  Foster, Scott D ^a,b   Verbyla, Arnas P ^a,b   Pitchford, Wayne S ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b CSIRO   (Australia)

Author keywords

Hierarchical model; LASSO; Marginal likelihood; Prediction distribution; Variance parameters

Indexed keywords

EID: 62249113520     PISSN: 13691473     EISSN: 1467842X     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2008.00526.x     Document Type: Article

References (17)

1. Andrews, D.F. Mallows, C.L. (1974). Scale mixtures of normal distributions. J. R. Statist. Soc. Ser. B Statist. Methodol. 36, 99 102.
2. Foster, S.D., Verbyla, A.P. Pitchford, W.S. (2008). A random model approach for the LASSO. Comput. Statist 23, 217 233.
3. Foster, S.D., Verbyla, A.P. Pitchford, W.S. (2007b). Incorporating LASSO effects into a mixed model for QTL detection. J. Agric. Biol. Environ. Statist. 12, 300 314.
4. Fu, W.J. (1998). Penalized regressions: The bridge versus the lasso. J. Comput. Graph. Statist. 7, 397 416.
5. Gelman, A., Carlin, J.B., Stern, H.S. Rubin, B.R. (1995). Bayesian data analysis. Texts in Statistical Science. New York : Chapman and HallCRC.
6. Grandvalet, Y. Canu, S. (1999). Outcomes of the equivalence of adaptive ridge with least absolute shrinkage. In : Advances in Neural Information Processing Systems 11: Proceedings of the 1998 Conference. eds M.S. Kearns, S.A. Solla, D.A. Cohn, pp. 445 451. Cambridge : MIT Press.
7. Hoerl, A.E. Kennard, R.W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12, 55 67.
8. Kiiveri, H.T. (2003). A Bayesian approach to variable selection when the number of variables is very large. In : Science and Statistics: A Festschrift for Terry Speed. ed. D.R. Goldstein, pp. 127 143. Lecture Notes - Monograph Series, vol. 30. Institute of Mathematical Statistics.
9. Kotz, S., Kozubowski, T.J. Podgórski, K. (2001). The Laplace distribution and generalizations. Boston : Birkhäuser.
10. Lindley, D.V. Smith, A.F.M. (1972). Bayes estimates for the linear model. J. R. Stat. Soc. Ser. B Statist. Methodol. 34, 1 41.
11. Miller, A. (2002). Subset Selection in Regression, 2nd edn. Monographs on Statistics and Applied Probability, vol. 95. London : Chapman & HallCRC.
12. Osborne, M.R., Presnell, B. Turlach, B.A. (2000). On the LASSO and its dual. J. Comput. Graph. Statist. 9, 319 337.
13. Robinson, G.K. (1991). That BLUP is a good thing: The estimation of random effects. Statist. Sci. 6, 15 51.
14. Searle, S.R., Casella, G. McCulloch, C.E. (1992). Variance Components. New York : John Wiley & Sons.
15. Stamey, T.A., Kabalin, J.N., McNeal, J.E., Johnstone, I.M., Freiha, F., Redwine, E.A. Yang, N. (1989). Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate, II: Radical prostatectomy treated patients. J. Urology 141, 1076 1083.
16. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. R. Statist. Soc. Ser. B Statist. Methodol. 58, 267 288.
17. Yuan, M. Lin, Y. (2005). Efficient empirical Bayes variable selection and estimation in linear models. J. Amer. Statist. Assoc. 100, 1215 1225.