Fast nonparametric quantile regressionwith arbitrary smoothing methods

Journal of Computational and Graphical Statistics

Volumn 20, Issue 2, 2011, Pages 510-526

  Hee Seok, Oh ^a   LEE, Thomas C M ^b   Nychka, Douglas W ^c  

^a Seoul National University   (South Korea)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c National Center for Atmospheric Research   (Brazil)

Author keywords

Bivariate quantile regression; Nonparametric regression; Pseudo data; Regression quantile; Wavelets

Indexed keywords

EID: 80051609064     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2010.10063     Document Type: Article

References (29)

1. Abramovich, F., and Benjamin, Y. (1995), Thresholding of Wavelet Coefficient as Multiple Hypotheses Testing Procedure. Wavelets and Statistics. Lecture notes in Statistics, Vol. 103, New York: Springer, pp. 5-14. [524]
2. Antoniadis, A., and Fan, J. (2001), "Regularization of Wavelet Approximations," Journal of the American Statistical Association, 96, 939-962. [523]
3. Bhattacharya, P. K., and Gangopadhyay, A. K. (1990), "Kernel and Nearest-Neighbor Estimation of a Conditional Quantile," The Annals of Statistics, 18, 1400-1415. [511,517]
4. Cantoni, E., and Ronchetti, E. (2001), "Resistant Selection of the Smoothing Parameter for Smoothing Splines," Statistics and Computing, 11, 141-146. [515]
5. Chaudhuri, P. (1991a), "Global Nonparametric Estimation of Conditional Quantile Functions and Their Derivatives," Journal of Multivariate Analysis, 39, 246-269. [511]
6. Chaudhuri, P. (1991b), "Nonparametric Estimates of Regression Quantiles and Their Local Bahadur Representation," The Annals of Statistics, 19, 760-777. [511]
7. Chaudhuri, P., and Loh, W. Y. (2002), "Nonparametric Estimation of Conditional Quantiles Using Quantile Regression Trees," Bernoulli, 8, 561-576. [511]
8. Cooley, D., Nychka, D., and Naveau, P. (2005), "Bayesian Spatial Modeling of Extreme Precipitation Return Levels," Journal of the American Statistical Association, 102, 824-840. [522]
9. Cox, D. D. (1983), "Asymptotics for M-Type Smoothing Splines," The Annals of Statistics, 11, 530-551. [515]
10. Friedman, J. H. (1991), "Multivariate Adaptive Regression Splines," The Annals of Statistics, 19, 1-67. [522]
11. Green, P. J., and Silverman, B. W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, London: Chapman & Hall. [518,520]
12. Gu, C. (1992), "Cross-Validating Non-Gaussian Data," Journal of Computational and Graphical Statistics, 2, 169-179. [518]
13. He, X., Ng, P., and Portnoy, S. (1998), "Bivariate Quantile Smoothing Splines," Journal of the Royal Statistical Society, Ser. B, 60, 537-550. [511,514,521,522]
14. Healy, M. J. R., Rasbash, J., and Yang, M. (1988), "Distribution-Free Estimation of Age-Related Centiles," Annals of Human Biology, 15, 17-22. [517,519]
15. Hendricks, W., and Koenker, R. (1992), "Hierarchical Spline Model for Conditional Quantiles and the Demand for Electricity," Journal of the American Statistical Society, 87, 58-68. [511]
16. Johnstone, I. M., and Silverman, B. W. (2005), "Empirical Bayes Selection of Wavelet Thresholds," The Annals of Statistics, 33, 1700-1752. [523]
17. Koenker, R. (2005), Quantile Regression, New York: Cambridge University Press. [511]
18. Koenker, R., and Bassett, G. (1978), "Regression Quantiles," Econometrica, 46, 33-50. [511]
19. Koenker, R., Ng, P., and Portnoy, S. (1994), "Quantile Smoothing Splines," Biometrika, 81, 673-680. [511,514,519]
20. Lejeune, M. G., and Sarda, P. (1988), "Quantile Regression: A Nonparametric Approach," Computational Statistics and Data Analysis, 6, 229-239. [511]
21. Li, Y., Liu, Y., and Zhu, J. (2007), "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, 102, 255-268. [511]
22. Nason, G. P. (1998), "WaveThresh3 Software," Dept. of Mathematics, University of Bristol, Bristol, U.K. [523]
23. Nychka, D. W., Gray, G., Haaland, P., Martin, D., and O'Connell, M. (1995), "A Nonparametric Regression Approach to Syringe Grading for Quality Improvement," Journal of the American Statistical Association, 90, 1171-1178. [514,517,518]
24. Oh, H.-S., Nychka, D. W., and Lee, T. C. M. (2007), "The Role of Pseudo Data for Robust Smoothing With Application to Wavelet Regression," Biometrika, 94, 893-904. [511,515,516]
25. Truong, Y. K. N. (1989), "Asymptotic Properties of Kernel Estimators Based on Local Medians," The Annals of Statistics, 17, 606-617. [511]
26. Yu, K. (1999), "Smoothing Regression Quantile by Combining k-NN With Local Linear Fitting," Statistica Sinica, 9, 759-771. [511,517,519]
27. Yu, K., and Jones, M. C. (1998), "Local Linear Regression Quantile Estimation," Journal of the American Statistical Association, 93, 228-238. [511]
28. Yu, K., Lu, Z., and Stander, J. (2003), "Quantile Regression: Application and Current Research Areas," The Statistician, 52, 331-350. [511]
29. Yuan, M(2006), "GACV for Quantile Smoothing Splines," Computational Statistics and Data Analysis, 50, 813-829. [517]