An interior point algorithm for nonlinear quantile regression

Journal of Econometrics

Volumn 71, Issue 1-2, 1996, Pages 265-283

  Koenker, Roger ^a   Park, Beum J ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Interior point algorithms; Linear programming; Nonlinear programming; Nonlinear regression; Quantile regression

Indexed keywords

EID: 0001242354     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-4076(96)84507-6     Document Type: Article

References (44)

1. Bard, Y., 1970, Comparison of gradient methods for the solution of nonlinear parameter estimation problems, Journal of Numerical Analysis 7, 157-186.
2. 1 norm, Communications of the ACM 17, 319-320.
3. 1 problems, ACM Transactions on Mathematical Software 6, 594-608.
4. 1 data fitting, in: A. Dold and B. Eckman, eds., Lecture notes in mathematics and numerical analysis (Springer-Verlag, New York, NY) 48-58.
5. 1 estimates, Computational Statistics and Data Analysis 14, 207-211.
6. Bayer, D.A. and J.C. Lagarias, 1991, Karmarkar's linear programming algorithm and Newton's method, Mathematical Programming 50, 291-330.
7. Beale, E.M.L., 1958, On an iterative method of finding a local minimum of a function of more than one variable, Technical report no. 25 (Statistical Techniques Research Group, Princeton University, Princeton, NJ).
8. Becker, R.A., J.M. Chambers, and A.R. Wilks, 1988, The new S language (Wadsworth, Pacific Grove, CA).
9. Biggs, M.C., 1971, Minimization algorithms making use of non-quadratic properties of the objective function, Journal of Institutional Mathematical Applications 8, 315-327.
10. Brown, K.M. and J.E. Dennis, 1971, New computational algorithms for minimizing a sum of squares of nonlinear functions, Report no. 71-6 (Department of Computer Science, Yale University, New Haven, CT).
11. 1 algorithm, Technical report no CS-85-34 (Department of Computer Science, University of Waterloo, Waterloo).
12. Chamberlain, G., 1990, Quantile regression, censoring and the structure of wages, Invited paper presented at the 6th World Congress of the Econometric Society.
13. Charnes, A., W.W. Cooper, and R.O. Ferguson, 1955, Optimal estimation of executive compensation by linear programming, Management Science 1, 138-151.
14. Colville, A.R., 1968, A comparative study of nonlinear programming codes. Report no. 320 2949 (IBM Scientific Center, New York, NY).
15. 1-norm and related methods (North-Holland, Amsterdam).
16. 1-approximation, SIAM Journal of Numerical Analysis 16, 70-86.
17. Fiacco, A.V. and G.P. McCormick, 1965, Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York, NY).
18. Fox, P.A., 1984, The PORT mathematical subroutine library (Bell Laboratories, Murray Hill, NJ).
19. Gay, D.M., 1984, A trust region approach to linearly constrained optimization, in: F.A. Lootsma, ed., Numerical analysis, Proceedings, Dundee 1983 (Springer, Berlin) 171-189.
20. Gill, P.E., W. Murray, M.A. Saunders, J.A. Tomlin, and M.M. Wright, 1986, On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method, Mathematical Programming 36, 183-209.
21. Gutenbrunner, C. and J. Jurečková, 1992, Regression rank scores and regression quantiles, Annals of Statistics 20, 305-330.
22. Gutenbrunner, C., J. Jurečková, A. Koenker, and S. Portnoy, 1993, Tests of linear hypotheses based on regression rank scores, Journal of Nonparametric Statistics 2, 307-331.
23. Hájek, J. and Z. Šidák, 1967, Theory of rank tests (Academia, Prague).
24. Horowitz, J. and G. Neumann, 1987, Semiparametric estimation of employment duration models, Econometric Reviews 6, 5-46.
25. Jurečková, J. and B. Procházka, 1993, Regression quantiles and trimmed least squares estimators in nonlinear regression models, Journal of Nonparametric Statistics, forthcoming.
26. Koenker, R. and V. d'Orey, 1987, Computing regression quantiles, Applied Statistics 36, 383-390.
27. Koenker, R.W. and G.W. Bassett, 1978, Regression quantiles, Econometrica 46, 33-50.
28. Kowalik, J.S. and M.R. Osborne, 1968, Methods for unconstrained optimization problems (Elsevier Science, New York, NY).
29. Meketon, M., 1986, Least absolute value regression, Technical report (AT&T Bell Laboratories, Holmdel, NJ).
30. 1 optimization, SIAM Journal of Scientific and Statistical Computing 1, 207-224.
31. Nelder, J. and R. Mead, 1965, A simplex method for function minimization, Computer Journal 7, 308-313.
32. 1-norm, Annals of Statistics 10, 316-319.
33. Osborne, M.R., 1972. Some aspects of nonlinear least squares calculations, in: E.A. Lootsma, ed., Numerical methods for nonlinear optimization (Academic Press, New York, NY) 171-189.
34. 1 approximation, Computer Journal 14, 184-188.
35. Powell, J., 1991, Estimation of monotone regression models under quantile restrictions, in: W.A. Barnett, J. Powell, and G. Tauchen eds., Nonparametric and semiparametric methods in econometrics and statistics (Cambridge University Press, New York, NY).
36. Powell, J., 1986, Censored regression quantiles. Journal of Econometrics 32, 143-155.
37. Powell, M.J.D., 1962, An iterative method for finding stationary values of a function of several variables, Computer Journal 5, 147-151.
38. Rosenbrock, H.H., 1960, An automatic method for finding the greatest or least value of a function, Computer Journal 3, 175-184.
39. Ruppert, D. and R.J. Carroll, 1980, Trimmed least square estimation in the linear models, Journal of the American Statistical Association 75, 828-838.
40. Vanderbei, R.J., M.J. Meketon, and B.A. Freedman, 1986, A modification of Karmarkar's linear programming algorithm, Algorithmica 1, 395-407.
41. Wagner, H.M., 1959, Linear programming techniques for regression analysis, Journal of American Statistical Association 54, 206-212.
42. Weiss, A., 1991, Estimating nonlinear dynamic models using least absolute error estimation, Econometric Theory 7, 46-68.
43. White H., 1991, Nonparametric estimation of conditional quantiles using neural networks, Unpublished paper.
44. 1 approximation, SIAM Journal of Scientific & Statistical Computing 7, 105-122.