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Weighted local linear CQR for varying-coefficient models with missing covariates

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  • Linjun Tang
  • Zhangong Zhou

Abstract

This paper considers composite quantile regression (CQR) estimation and inference for varying-coefficient models with missing covariates. We propose the weighted local linear CQR (WLLCQR) estimators for unknown coefficient function when selection probabilities are known, estimated nonparametrically or parametrically. Theoretical and numerical results demonstrate that the WLLCQR estimators with estimating weights are more efficient than the true weights. Moreover, a goodness-of-fit test based on the WLLCQR fittings is developed to test whether the coefficient functions are actually varying. The finite-sample performance of the proposed methodology is assessed by simulation studies. A real data set is conducted to illustrate our proposed method. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Linjun Tang & Zhangong Zhou, 2015. "Weighted local linear CQR for varying-coefficient models with missing covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 583-604, September.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:3:p:583-604
    DOI: 10.1007/s11749-014-0425-z
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    Cited by:

    1. Jun Jin & Tiefeng Ma & Jiajia Dai & Shuangzhe Liu, 2021. "Penalized weighted composite quantile regression for partially linear varying coefficient models with missing covariates," Computational Statistics, Springer, vol. 36(1), pages 541-575, March.
    2. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    3. 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.
    4. Jing Sun, 2020. "An improvement on the efficiency of complete-case-analysis with nonignorable missing covariate data," Computational Statistics, Springer, vol. 35(4), pages 1621-1636, December.
    5. Fan, Guo-Liang & Xu, Hong-Xia & Liang, Han-Ying, 2019. "Dimension reduction estimation for central mean subspace with missing multivariate response," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    6. Puying Zhao & Hui Zhao & Niansheng Tang & Zhaohai Li, 2017. "Weighted composite quantile regression analysis for nonignorable missing data using nonresponse instrument," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 189-212, April.
    7. ChunJing Li & Yun Li & Xue Ding & XiaoGang Dong, 2020. "DGQR estimation for interval censored quantile regression with varying-coefficient models," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-17, November.
    8. Zhangong Zhou & Linjun Tang, 2019. "Testing for parametric component of partially linear models with missing covariates," Statistical Papers, Springer, vol. 60(3), pages 747-760, June.
    9. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    10. Sun, Jing & Sun, Qihang, 2015. "An improved and efficient estimation method for varying-coefficient model with missing covariates," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 296-303.
    11. Shen, Yu & Liang, Han-Ying, 2018. "Quantile regression for partially linear varying-coefficient model with censoring indicators missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 1-18.

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