Simultaneous Estimation of Multiple Conditional Regression Quantiles
Tóm tắt
In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over (0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines to fit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.
Tài liệu tham khảo
Guo, M., Zhou, L., Huang, J. Z., Härdle, W. K. Functional data analysis of generalized regression quantiles. Statistics and Computing, 25(2): 189–202 (2015)
Guo, J., Tang, M., Tian, M., Zhu, K. Variable selection in high-dimensional partially linear additive models for composite quantile regression. Computational Statistics and Data Analysis, 65: 56–67 (2013)
He, X., Ng, P. COBS: qualitatively constrained smoothing via linear programming. Computational Statistics, 14(3): 315–338 (1999)
He, X., Ng, P. Quantile splines with several covariates. Journal of Statistical Planning and Inference, 75(2): 343–352 (1999)
He, X., Ng, P., Portnoy, S. Bivariate quantile smoothing splines. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60(3): 537–550 (1998)
Hendricks, W., Koenker, R. Hierarchical spline models for conditional quantiles and the demand for electricity. Journal of the American Statistical Association, 87(417): 58–68 (1992)
Koenker, R., Bassett Jr, G. Regression quantiles. Econometrica: journal of the Econometric Society, 33–50 (1978)
Koenker, R., Ng, P., Portnoy, S. Quantile smoothing splines. Biometrika, 81(4): 673–680 (1994)
Li, Y., Liu, Y., Zhu, J. Quantile regression in reproducing kernel Hilbert spaces. Journal of the American Statistical Association, 102(477): 255–268 (2007)
Li, Y., Zhu, J. L1-Norm Quantile Regression. Journal of Computational and Graphical Statistics, 17(1): 163–185 (2008)
Liu, Y., Wu, Y. Simultaneous multiple non-crossing quantile regression estimation using kernel constraints. Journal of nonparametric statistics, 23(2): 415–437 (2011)
Schlossmacher, E. J. An iterative technique for absolute deviations curve fitting. Journal of the American Statistical Association, 68(344): 857–859 (1973)
Schnabel, S. K., Eilers, P. H. Simultaneous estimation of quantile curves using quantile sheets. Acta Advances in Statistical Analysis, 97(1): 77–87 (2013)
Tian, M. Z., Tang, M. L., Chan, P. S. Semiparametric quantile modelling of hierarchical data. Acta Mathematica Sinica, English Series, 25(4): 597–616 (2009)
Tokdar, S., Kadane, J. B. Simultaneous linear quantile regression: A semiparametric bayesian approach. Bayesian Analysis, 7(1): 51–72 (2012)
Yu, K., Jones, M. C. Local linear quantile regression. Journal of the American statistical Association, 93(441): 228–237 (1998)
Zou, H., Yuan, M. Regularized simultaneous model selection in multiple quantiles regression. Computational Statistics and Data Analysis, 52(12): 5296–5304 (2008)