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A general framework for quantile estimation with incomplete data

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  • Peisong Han
  • Linglong Kong
  • Jiwei Zhao
  • Xingcai Zhou

Abstract

Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable of dealing with many different missingness settings. We mainly study three of them: estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; estimating the conditional quantile of a fully observed response while the covariates are partially available; estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The method proposed allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established by using empirical process theory.

Suggested Citation

  • Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:2:p:305-333
    DOI: 10.1111/rssb.12309
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    References listed on IDEAS

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    3. Liang, Jinwen & Härdle, Wolfgang Karl & Tian, Maozai, 2023. "Imputed quantile tensor regression for near-sited spatial-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. Hairu Wang & Zhiping Lu & Yukun Liu, 2023. "Score test for missing at random or not under logistic missingness models," Biometrics, The International Biometric Society, vol. 79(2), pages 1268-1279, June.
    6. Shi, Jianwei & Qin, Guoyou & Zhu, Huichen & Zhu, Zhongyi, 2021. "Communication-efficient distributed M-estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    8. Su, Miaomiao & Wang, Qihua, 2022. "A convex programming solution based debiased estimator for quantile with missing response and high-dimensional covariables," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    9. Lu, Wenqi & Qin, Guoyou & Zhu, Zhongyi & Tu, Dongsheng, 2021. "Multiply robust subgroup identification for longitudinal data with dropouts via median regression," Journal of Multivariate Analysis, Elsevier, vol. 181(C).

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