A finite smoothing algorithm for quantile regression

Journal of Computational and Graphical Statistics

Volumn 16, Issue 1, 2007, Pages 136-164

  Chen, Colin ^a  

^a SAS INSTITUTE INC   (United States)

Author keywords

Complexity; Interior point; Linear programming; Median regression; Preprocessing; Quantile regression; Simplex

Indexed keywords

EID: 34147195491     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186007X180336     Document Type: Article

References (21)

1. 1 Linear Approximation," SIAM Journal of Numerical Analysis, 10, 839-848.
2. Chen, C., and Wei, Y. (2005), "Computational Issues on Quantile Regression," Sankhya, 67, 399-417.
3. Clark D. I., and Osborne, M. R. (1986), "Finite Algorithms for Huber's M-estimator," SIAM Journal of Scientific Statistical Computing, 7, 72-85.
4. Huber, P. J. (1973), "Robust Regression: Asymptotics, Conjectures, and Monte Carlo," The Annals of Statistics, 1, 799-821.
5. Hunter, D. R., and Lange, K. (2000), "Quantile Regression via An MM Algorithm," Journal of Computational and Graphical Statistics, 9, 66-77.
6. Karmarkar, N. (1984), "A New Polynomial-Time Algorithm for Linear Programming," Combinatorica, 4, 373-395.
7. Koenker, R. (2005), Quantile Regression, New York: Cambridge University Press.
8. Koenker, R., and Bassett, Jr. G. (1978), "Regression Quantiles," Econometrica, 46, 33-50.
9. Koenker, R., and d'Orey, V. (1987), "Algorithm AS 229: Computing Regression Quantiles," Applied Statistics, 36, 383-393.
10. Koenker, R., and d'Orey, V. (1994), "Remark AS R92: A Remark on Algorithm AS 229: Computing Dual Regression Quantiles and Regression Rank Scores," Applied Statistics, 43, 410-414.
11. Koenker, R., and Ng, P. (2005), "Frisch-Newton Algorithm for Sparse Quantile Regression," Acta Mathematicae Applicatae Sinica (English series), 21, 225-236.
12. Koenker, R., and Park, B. J. (1996), "An Interior Point Algorithm for Nonlinear Quantile Regression," Journal of Econometrics, 71, 265-283.
13. Lange, K., Hunter, D. R., and Yang, I. (2000), "Optimization Transfer Using Surrogate Objective Function," Journal of Computational and Graphical Statistics, 9, 1-20.
14. Lustig, I. J., Marsden, R. E., and Shanno, D. F. (1992), "On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming," SIAM Journal of Optimization, 2, 435-449.
15. 1 Estimation," SIAM Journal of Optimization, 3, 223-235.
16. Mehrotra, S. (1992), "On the Implementation of A Primal-Dual Interior Point Method," SIAM Journal of Optimization, 2, 575-601.
17. Osborne, M. R. (1992), "An Effective Method for Computing Regression Quantiles," IMA Journal of Numerical Analysis, 12, 151-166.
18. Pinar, M. C., and Hartmann, W. M. (2004), "Huber Approximation for Nonlinear LI Estimation," Preprint.
19. Portnoy, S., and Koenker, R. (1997), "The Gaussian Hare and the Laplacian Tortoise: Computation of Squared-Error vs. Absolute-Error Estimators," Statistical Science, 12, 279-300.
20. Roos, C., Terlaky, T., and Vial, J.-Ph. (1997), Theory and Algorithms for Linear Optimization, Chichester, England: Wiley.
21. Vanderbei, R. J., Meketon, M. J., and Freedman, B. A. (1986), "A Modification of Karmarkar's Linear Programming Algorithm," Algorithmica, 1, 395-407.