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http://dx.doi.org/10.5351/KJAS.2016.29.5.773

A comparison study of multiple linear quantile regression using non-crossing constraints  

Bang, Sungwan (Department of Mathematics, Korea Military Academy)
Shin, Seung Jun (Department of Statistics, Korea University)
Publication Information
The Korean Journal of Applied Statistics / v.29, no.5, 2016 , pp. 773-786 More about this Journal
Abstract
Multiple quantile regression that simultaneously estimate several conditional quantiles of response given covariates can provide a comprehensive information about the relationship between the response and covariates. Some quantile estimates can cross if conditional quantiles are separately estimated; however, this violates the definition of the quantile. To tackle this issue, multiple quantile regression with non-crossing constraints have been developed. In this paper, we carry out a comparison study on several popular methods for non-crossing multiple linear quantile regression to provide practical guidance on its application.
Keywords
multiple linear quantile regression; non-crossing; linear programming;
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1 Bondell, H. D., Reich, B. J., and Wang, H. (2010). Noncrossing quantile regression curve estimation, Biometrika, 97, 825-838.   DOI
2 Cole, T. J. and Green, P. J. (1992). Smoothing reference centile curves: the LMS method and penalized likelihood, Statistics in Medicine, 11, 1305-1319.   DOI
3 He, X. (1997). Quantile curves without crossing, The American Statistician, 51, 186-192.
4 Heagerty, P. J. and Pepe, M. S. (1999). Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children, Journal of the Royal Statistical Society: Series C (Applied Statistics), 48, 533-551.   DOI
5 Hendricks, W. and Koenker, R. (1992). Hierarchical spline models for conditional quantiles and the demand for electricity, Journal of the American Statistical Association, 87, 58-68. Journal of Economic Perspectives, 15, 43-56.
6 Johnson, R. W. (1996). Fitting percentage of body fat to simple body measurements, Journal of Statistics Education, 4, 265-266.
7 Koenker, R. (2005). Quantile Regression, Cambridge university press, New York.
8 Koenker, R. and Bassett, Jr, G. (1978). Regression quantiles, Econometrica: Journal of the Econometric Society, 46 33-50.   DOI
9 Koenker, R. and Geling, O. (2001). Reappraising medfly longevity: a quantile regression survival analysis, Journal of the American Statistical Association, 96, 458-468.   DOI
10 Koenker, R. and Hallock, K. (2001). Quantile regression: an introduction, Journal of Economic Perspectives, 15, 43-56.   DOI
11 Koenker, R., Ng, P., and Portnoy, S. (1994). Quantile smoothing splines, Biometrika, 81, 673-680.   DOI
12 Li, Y., Liu, Y., and Zhu, J. (2007). Quantile regression in reproducing kernel Hilbert spaces, Journal of the American Statistical Association, 102, 255-268.   DOI
13 Liu, Y. and Wu, Y. (2011). Simultaneous multiple non-crossing quantile regression estimation using kernel constraints, Journal of Nonparametric Statistics, 23, 415-437.   DOI
14 Wang, H. and He, X. (2007). Detecting differential expressions in GeneChip microarray studies: a quantile approach, Journal of the American Statistical Association, 102, 104-112.   DOI
15 Shim, J., Hwang, C., and Seok, K. H. (2009). Non-crossing quantile regression via doubly penalized kernel machine, Computational Statistics, 24, 83-94.   DOI
16 Takeuchi, I. and Furuhashi, T. (2004). Non-crossing quantile regressions by SVM, In Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on, 1, IEEE.
17 Takeuchi, I., Le, Q. V., Sears, T. D., and Smola, A. J. (2006). Nonparametric quantile estimation, Journal of Machine Learning Research, 7, 1231-1264.
18 Wu, Y. and Liu, Y. (2009). Stepwise multiple quantile regression estimation using non-crossing constraints, Statistics and Its Interface, 2, 299-310.   DOI
19 Yang, S. (1999). Censored median regression using weighted empirical survival and hazard functions, Journal of the American Statistical Association, 94, 137-145.   DOI