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Quantile regression and variable selection of partial linear single-index model

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Listed:
  • Yazhao Lv
  • Riquan Zhang
  • Weihua Zhao
  • Jicai Liu
Abstract
Partial linear single-index model (PLSIM) is a flexible and applicable model when investigating the underlying relationship between the response and the multivariate covariates. Most previous studies on PLSIM concentrated on mean regression, based on least square or likelihood approach. In contrast to this method, in this paper, we propose minimizing average check loss estimation (MACLE) procedure to conduct quantile regression of PLSIM. We construct an initial consistent quantile regression estimator of the parametric part base multi-dimensional kernels, and further promote the estimation efficiency to the optimal rate. We discuss the optimal bandwidth selection method and establish the asymptotic normality of the proposed MACLE estimators. Furthermore, we consider an adaptive lasso penalized variable selection method and establish its oracle property. Simulation studies with various distributed error and a real data analysis are conducted to show the promise of our proposed methods. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:2:p:375-409
    DOI: 10.1007/s10463-014-0457-x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. 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.
    3. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    5. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    8. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. 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.
    11. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    12. Fan, Yan & Härdle, Wolfgang Karl & Wang, Weining & Zhu, Lixing, 2013. "Composite quantile regression for the single-index model," SFB 649 Discussion Papers 2013-010, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    14. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
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    Cited by:

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    2. 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.
    3. Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    4. Ke Wang & Dehui Wang, 2024. "Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors," Statistical Papers, Springer, vol. 65(7), pages 4201-4241, September.
    5. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    6. Myeonggyun Lee & Andrea B. Troxel & Mengling Liu, 2024. "Partial-linear single-index transformation models with censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 701-720, October.
    7. 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.
    8. Zou, Yuye & Wu, Chengxin, 2023. "Composite quantile regression analysis of survival data with missing cause-of-failure information and its application to breast cancer clinical trial," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    9. Hong-Xia Xu & Zhen-Long Chen & Jiang-Feng Wang & Guo-Liang Fan, 2019. "Quantile regression and variable selection for partially linear model with randomly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1137-1160, August.

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