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Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

Author

Listed:
  • Jingxuan Guo

    (School of Statistics and Data Science, Beijing Wuzi University, Beijing 101149, China
    The first two authors contributed equally to this work.)

  • Fuguo Liu

    (School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China
    School of Mathematics and Data Science, Changji University, Changji 831100, China
    The first two authors contributed equally to this work.)

  • Wolfgang Karl Härdle

    (Department of Information Management and Finance, National Yang Ming Chiao Tung University, Taiwan 30010, China
    Institute Digital Assets, Academy Economic Sciences, 010374 Bucharest, Romania
    School of Business and Economics, Humboldt-Universität zu Berlin, 10117 Berlin, Germany)

  • Xueliang Zhang

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

  • Kai Wang

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

  • Ting Zeng

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

  • Liping Yang

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

  • Maozai Tian

    (Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China)

Abstract

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles.

Suggested Citation

  • Jingxuan Guo & Fuguo Liu & Wolfgang Karl Härdle & Xueliang Zhang & Kai Wang & Ting Zeng & Liping Yang & Maozai Tian, 2023. "Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression," Mathematics, MDPI, vol. 11(24), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4906-:d:1296805
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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