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Quantile regression and variable selection for partially linear model with randomly truncated data

Author

Listed:
  • Hong-Xia Xu

    (Zhejiang Gongshang University
    Anhui Polytechnic University)

  • Zhen-Long Chen

    (Zhejiang Gongshang University)

  • Jiang-Feng Wang

    (Zhejiang Gongshang University)

  • Guo-Liang Fan

    (Anhui Polytechnic University)

Abstract

This paper focuses on the problem of estimation and variable selection for quantile regression (QR) of partially linear model (PLM) where the response is subject to random left truncation. We propose a three-stage estimation procedure for parametric and nonparametric parts based on the weights which are random quantities and determined by the product-limit estimates of the distribution function of truncated variable. The estimators obtained in the second and third stages are more efficient than the initial estimators in the first stage. Furthermore, we propose a variable selection procedure for the QR of PLM by combining the estimation method with the smoothly clipped absolute deviation penalty to get sparse estimation of the regression parameter. The oracle properties of the variable selection approach are established. Simulation studies are conducted to examine the performance of our estimators and variable selection method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0867-3
    DOI: 10.1007/s00362-016-0867-3
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    References listed on IDEAS

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    Cited by:

    1. Aifen Feng & Xiaogai Chang & Youlin Shang & Jingya Fan, 2022. "Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 10(24), pages 1-13, December.

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