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Two step composite quantile regression for single-index models

Listed author(s):
  • Jiang, Rong
  • Zhou, Zhan-Gong
  • Qian, Wei-Min
  • Chen, Yong
Registered author(s):

    This paper is concerned with composite quantile regression for single-index models. Under mild conditions, we show that the linear composite quantile regression offers a consistent estimate of the index parameter vector. With a root-n consistent estimate of the index vector, the unknown link function can be estimated by local composite quantile regression. This procedure enables us to reduce the computational cost and is also appealing in high-dimensional data analysis. We show that the resulting estimator of the composite quantile function performs asymptotically as efficiently as if the true value of the index vector is known. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 64 (2013)
    Issue (Month): C ()
    Pages: 180-191

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    Handle: RePEc:eee:csdana:v:64:y:2013:i:c:p:180-191
    DOI: 10.1016/j.csda.2013.03.014
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    1. Ma, Shuangge & Kosorok, Michael R., 2005. "Robust semiparametric M-estimation and the weighted bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 190-217, September.
    2. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    3. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    4. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    7. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    8. Chamberlain, Gary & Imbens, Guido W, 2003. "Nonparametric Applications of Bayesian Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 12-18, January.
    9. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    10. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    11. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
    12. Yanlin Tang & Huixia Wang & Xuming He & Zhongyi Zhu, 2012. "An informative subset-based estimator for censored quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 635-655, December.
    13. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    14. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(04), pages 730-768, August.
    15. Xu, Peirong & Zhu, Lixing, 2012. "Estimation for a marginal generalized single-index longitudinal model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 285-299.
    16. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69.
    17. Wang, Qihua & Xue, Liugen, 2011. "Statistical inference in partially-varying-coefficient single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 1-19, January.
    18. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    19. Wei Lin & K. B. Kulasekera, 2007. "Identifiability of single-index models and additive-index models," Biometrika, Biometrika Trust, vol. 94(2), pages 496-501.
    20. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346.
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