IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v83y2020i5d10.1007_s00184-019-00744-3.html
   My bibliography  Save this article

Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses

Author

Listed:
  • Xianwen Ding

    (Jiangsu University of Technology)

  • Jiandong Chen

    (Jiangsu University of Technology)

  • Xueping Chen

    (Jiangsu University of Technology
    Nankai University)

Abstract

The paper concerns the regularized quantile regression for ultrahigh-dimensional data with responses missing not at random. The propensity score is specified by the semiparametric exponential tilting model. We use the Pearson Chi-square type test statistic for identification of the important features in the sparse propensity score model, and employ the adjusted empirical likelihood method for estimation of the parameters in the reduced model. With the estimated propensity score model, we suggest an inverse probability weighted and penalized objective function for regularized estimation using the nonconvex SCAD penalty and MCP functions. Assuming the propensity score model is of low dimension, we establish the oracle properties of the proposed regularized estimators. The new method has several desirable advantages. First, it is robust to heavy-tailed errors or potential outliers in the responses. Second, it can accommodate nonignorable nonresponse data. Third, it can deal with ultrahigh-dimensional data with heterogeneity. Simulation study and real data analysis are given to examine the finite sample performance of the proposed approaches.

Suggested Citation

  • Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:5:d:10.1007_s00184-019-00744-3
    DOI: 10.1007/s00184-019-00744-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-019-00744-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-019-00744-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lyu Ni & Fang Fang & Fangjiao Wan, 2017. "Adjusted Pearson Chi-Square feature screening for multi-classification with ultrahigh dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 805-828, November.
    2. Lyu Ni & Fang Fang, 2016. "Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 515-530, September.
    3. Qin J. & Leung D. & Shao J., 2002. "Estimation With Survey Data Under Nonignorable Nonresponse or Informative Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 193-200, March.
    4. 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.
    5. 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.
    6. repec:mpr:mprres:8160 is not listed on IDEAS
    7. Jiwei Zhao & Jun Shao, 2015. "Semiparametric Pseudo-Likelihoods in Generalized Linear Models With Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1577-1590, December.
    8. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
    9. Sherwood, Ben, 2016. "Variable selection for additive partial linear quantile regression with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 206-223.
    10. Qihua Wang & Yongjin Li, 2018. "How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 324-346, June.
    11. Ted Chang & Phillip S. Kott, 2008. "Using calibration weighting to adjust for nonresponse under a plausible model," Biometrika, Biometrika Trust, vol. 95(3), pages 555-571.
    12. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    13. Jun Shao & Lei Wang, 2016. "Semiparametric inverse propensity weighting for nonignorable missing data," Biometrika, Biometrika Trust, vol. 103(1), pages 175-187.
    14. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    15. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    16. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    17. Danyang Huang & Runze Li & Hansheng Wang, 2014. "Feature Screening for Ultrahigh Dimensional Categorical Data With Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 237-244, April.
    18. Zhaoping Hong & Yuao Hu & Heng Lian, 2013. "Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 887-908, October.
    19. Lai, Peng & Liu, Yiming & Liu, Zhi & Wan, Yi, 2017. "Model free feature screening for ultrahigh dimensional data with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 201-216.
    20. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    21. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Jing & Wang, Qihua & Kang, Jian, 2020. "Feature screening under missing indicator imputation with non-ignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    2. 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.
    3. Li, Mengyan & Ma, Yanyuan & Zhao, Jiwei, 2022. "Efficient estimation in a partially specified nonignorable propensity score model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Shonosuke Sugasawa & Kosuke Morikawa & Keisuke Takahata, 2022. "Bayesian semiparametric modeling of response mechanism for nonignorable missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 101-117, March.
    5. Zhao, Jun & Chen, Yingyu & Zhang, Yi, 2018. "Expectile regression for analyzing heteroscedasticity in high dimension," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 304-311.
    6. Xiang Zhang & Yichao Wu & Lan Wang & Runze Li, 2016. "Variable selection for support vector machines in moderately high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 53-76, January.
    7. Wang, Lei & Zhao, Puying & Shao, Jun, 2021. "Dimension-reduced semiparametric estimation of distribution functions and quantiles with nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    8. Pengfei Li & Jing Qin & Yukun Liu, 2023. "Instability of inverse probability weighting methods and a remedy for nonignorable missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3215-3226, December.
    9. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    11. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    12. Zhan Liu & Chun Yip Yau, 2022. "A propensity score adjustment method for longitudinal time series models under nonignorable nonresponse," Statistical Papers, Springer, vol. 63(1), pages 317-342, February.
    13. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    14. Zhaoping Hong & Yuao Hu & Heng Lian, 2013. "Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 887-908, October.
    15. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    16. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.
    17. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    18. Weirong Li & Wensheng Zhu, 2024. "Subgroup analysis with concave pairwise fusion penalty for ordinal response," Statistical Papers, Springer, vol. 65(6), pages 3327-3355, August.
    19. Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    20. Liu, Tianqing & Yuan, Xiaohui & Sun, Jianguo, 2021. "Weighted rank estimation for nonparametric transformation models with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:83:y:2020:i:5:d:10.1007_s00184-019-00744-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.