On the LASSO and its Dual

Journal of Computational and Graphical Statistics

Volumn 9, Issue 2, 2000, Pages 319-337

  Osborne, Michael R ^a   Presnell, Brett ^b   Turlach, Berwin A ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b University of Florida ^*  (United States)

^c UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Convex programming; Dual problem; Partial least squares; Penalized regression; Quadratic programming; Regression; Shrinkage; Subset selection; Variable selection

Indexed keywords

EID: 23044520947     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2000.10474883     Document Type: Article

References (19)

1. Brown, P. J. (1993), Measurement, Regression, and Calibration, Oxford: Clarendon Press.
2. Chen, S. S., Donoho, D. L., and Saunders, M. A. (1999), “Atomic Decomposition by Basis Pursuit,” SIAM Journal on Scientific Computing, 20, 33-61 (http://www-stat.Stanford.edu/~donoho/Reports/1995/30401.ps.Z).
3. Clark, D. I., and Osborne, M. R. (1988), “On Linear Restricted and Interval Least-Squares Problems,” IMA Journal of Numerical Analysis, 8, 23-36.
4. Frank, I. E., and Friedman, J. H. (1993), “A Statistical View of Some Chemometrics Regression Tools” (with discussion), Technometrics, 35, 109-148.
5. Fu, W. J. (1998), “Penalized Regression: The Bridge Versus the Lasso,” Journal of Computational and Graphical Statistics, 1, 397-416.
6. Gallant, A. R. (1987), Nonlinear Statistical Models, New York: Wiley.
7. Haagen, K., Bartholomew, D. J., Deistler, M. (eds) (1993), Statistical Modelling and Latent Variables, New York; Amsterdam: Elsevier/North-Holland.
8. Koch, I. (1996), “On the Asymptotic Performance of Median Smoothers in Image Analysis and Nonparametric Regression,” The Annals of Statistics, 24, 1648-1666.
9. Meyer, M. C. (1999), “An Extension of the Mixed Primal-Dual Bases Algorithm to the Case of More Constraints Than Dimensions,” Journal of Statistical Planning and Inference, 81, 13-31.
10. Miller, A. J. (1990), Subset Selection in Regression, vol. 40 of Monographs on Statistics and Applied Probability, London: Chapman and Hall.
11. Nash, S. G., and Sofer, A. (1996), Linear and Nonlinear Programming, New York: McGraw-Hill.
12. Osborne, M. R. (1985), Finite Algorithms in Optimization and Data Analysis, Wiley Series in Probability and Mathematical Statistics, Chichester: Wiley.
13. Osborne, M. R., Presnell, B., and Turlach, B. A. (1998), “Knot Selection for Regression Splines via the Lasso,” in Dimension Reduction, Computational Complexity, and Information, ed. S. Weisberg, vol. 30 of Computing Science and Statistics, Fairfax Station, VA: Interface Foundation of North America, pp. 44-49, (http://www.maths.uwa.edu.au/~berwin/psfiles/interface98.ps.gz).
14. Osborne, M. R., Presnell, B., and Turlach, B. A. (in press), “A New Approach to Variable Selection in Least Squares Problems,” IMA Journal of Numerical Analysis.
15. Rao, C. R. (1973), Linear Statistical Inference and Its Applications (2nd ed.), New York: Wiley.
16. Rockafellar, R. T. (1970), Convex Analysis, vol. 28 of Princeton Mathematical Series, Princeton, NJ: Princeton University Press.
17. Sardy, S., Bruce, A. G., and Tseng, P. (2000), “Block Coordinate Relaxation Methods for Nonparametric. Wavelet Denoising,” Journal of Computational and Graphical Statistics, 9, 361-379.
18. Stamey, T. A., Kabalin, J. N., McNeal, J. E., Johnstone, I. M., Freiha, F., Redwine, E. A., and Yang, N. (1989), “Prostate Specific Antigen in the Diagnosis and Treatment of Adenocarcinoma of the Prostate: II. Radical Prostatectomy Treated Patients,” Journal of Urology, 141, 1076-1083.
19. Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267-288.