Quantile Regression via an MM Algorithm

Journal of Computational and Graphical Statistics

Volumn 9, Issue 1, 2000, Pages 60-77

  Hunter, David R ^a   Lange, Kenneth ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

EM algorithm; Gauss Newton method; L1 regression; Majorization

Indexed keywords

EID: 23044517556     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2000.10474866     Document Type: Article

References (35)

1. Bassett, G., and Koenker, R. (1978), “Asymptotic Theory of Least Absolute Error Regression,” Journal of the American Statistical Association, 73, 618-622.
2. Bassett, G., and Koenker, R. (1982), “An Empirical Quantile Function for Linear Models with iid Errors,” Journal if the American Statistical Association, 77, 407-415.
3. Becker, M. P., Yang, I., and Lange, K. (1997), “EM Algorithms Without Missing Data,” Statistical Methods in Medical Research, 6, 37-53.
4. Borg, I., and Groenen, P. (1997), Modem Multidimensional Scaling, New York: Springer.
5. Buchinsky, M. (1995), “Quantile Regression, Box-Cox Transformation Model, and the U.S. Wage Structure,” Journal of Econometrics, 65, 109-154.
6. Casella, G., and Berger, R. L. (1990), Statistical Inference, Pacific Grove, CA: Wadsworth & Brooks/Cole.
7. Cole, T. J. (1988), “Fitting Smoothed Centile Curves to Reference Data,” Journal of the Royal Statistical Society, Series A, 151, 385-418.
8. de Leeuw, J. (1994), “Block-Relaxation Algorithms in Statistics,” in Information Systems and Data Analysis, eds. H. H. Bock et al., Berlin: Springer-Verlag, pp. 308-325.
9. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 39, 1-38.
10. Efron, B. (1991), “Regression Percentiles Using Asymmetric Squared Error Loss,” Statistica Sinica, 1, 93-125.
11. Eide, E., and Showalter, M. H. (1998), “The Effect of School Quality on Student Performance: A Quantile Regression Approach,” Economics Letters, 58, 345-350.
12. El-Attar, R. A., Vidyasagar, M., and Dutta, S. R. K. (1979), “An Algorithm for Li-norm Minimization With Application to Nonlinear LApproximation,” SIAM Journal of Numerical Analysis, 16, 70-86.
13. Erdogan, H., and Fessler, J. A. (1999), “Monotonic Algorithms for Transmission Tomography,” IEEE Transactions on Medical Imaging, 18, 801-814.
14. Ferguson, T. S. (1967), Mathematical Statistics: A Decision Theoretic Approach, New York: Academic Press.
15. He, X. (1997), “Quantile Curves Without Crossing,” The American Statistician, 51, 186-192.
16. Heiser, W. J. (1995), “Convergent Computation by Iterative Majorization,” in Recent Advances in Descriptive Multivariate Analysis, ed. W. J. Krzanowski, New York: Oxford University Press, pp. 157-189.
17. Kennedy, W. J. Jr., and Gentle, J. E. (1980), Statistical Computing, New York: Marcel Dekker.
18. Koenker, R., and Bassett, G. (1978), “Regression Quantiles,” Econometrica, 46, 33-50.
19. Koenker, R., and Bassett, G. (1982), “Robust Tests for Heteroscedasticity Based on Regression Quantiles,” Econometrica, 50,43-61.
20. Koenker, R., and Park, B. J. (1996), “An Interior Point Algorithm for Nonlinear Quantile Regression,” Journal of Econometrics, 71, 265-283.
21. Lange, K. (1995), “A Gradient Algorithm Locally Equivalent to the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 57, 425-437.
22. Lange, K., and Sinsheimer, J. (1993), “Normal/Independent Distributions and Their Applications in Robust Regression,” Journal of Computational and Statistical Graphics, 2, 175-198.
23. Lange, K., Hunter, D. R., and Yang, I. (2000), “Optimization Transfer Using Surrogate Objective Functions” (with discussion), Journal of Computational and Graphical Statistics, 9, 1-59.
24. Madsen, K., and Nielsen, H. B. (1990), “Finite Algorithms for Robust Linear Regression,” Bit, 30, 682-699.
25. McLachlan, G. J., and Krishnan, T. (1996), The EM Algorithm and Extensions, Wiley: New York.
26. p Approximation,” Computing, 12, 315-321.
27. Mosteller, F., and Tukey, J. W. (1977), Data Analysis and Regression: A Second Course in Statistics, Reading, MA: Addison-Wesley.
28. Ortega, J. M., and Rheinboldt, W. C. (1970), Iterative Solution of Nonlinear Equations in Several Variables, Orlando: Academic Press.
29. Portnoy, S., and Koenker, R. (1997), “The Gaussian Hare and the Laplacian Tortoise: Computability of Squared-Error Versus Absolute-Error Estimators,” Statistical Science, 12, 279-300.
30. Powell, J. L. (1986), “Censored Regression Quantiles,” Journal of Econometrics, 32, 143-155.
31. Press, W., Flannery, B., Teukolsky, S., and Vetterling, W. (1986), Numerical Recipes, Cambridge: Cambridge University Press.
32. Rousseeuw, P. J., and Leroy, A. M. (1987), Robust Regression and Outlier Detection, New York: Wiley.
33. Schlossmacher, E. J. (1973), “An Iterative Technique for Absolute Deviations Curve Fitting,” Journal of the American Statistical Association, 68, 857-859.
34. Taylor, J. W., and Bunn, D. W. (1998), “Combining Forecast Quantiles Using Quantile Regression: Investigating the Derived Weights, Estimator Bias and Imposing Constraints,” Journal of Applied Statistics, 25, 193-206.
35. Verboon, P. (1994), A Robust Approach to Nonlinear Multivariate Analysis, Leiden, the Netherlands: DSWO Press.