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Two step composite quantile regression for single-index models

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  • Jiang, Rong
  • Zhou, Zhan-Gong
  • Qian, Wei-Min
  • Chen, Yong

Abstract

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.

Suggested Citation

  • Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    • 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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    2. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    3. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    4. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    5. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    6. Xie, Qichang & Sun, Qiankun, 2019. "Computation and application of robust data-driven bandwidth selection for gradient function estimation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 274-293.
    7. Xiaohui Yuan & Yong Li & Xiaogang Dong & Tianqing Liu, 2022. "Optimal subsampling for composite quantile regression in big data," Statistical Papers, Springer, vol. 63(5), pages 1649-1676, October.
    8. Rong Jiang & Wei-Min Qian & Jing-Ru Li, 2014. "Testing in linear composite quantile regression models," Computational Statistics, Springer, vol. 29(5), pages 1381-1402, October.
    9. Hong-Xia Xu & Guo-Liang Fan & Zhen-Long Chen & Jiang-Feng Wang, 2018. "Weighted quantile regression and testing for varying-coefficient models with randomly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 565-588, October.
    10. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    11. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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