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Instrument search in pseudo-likelihood approach for nonignorable nonresponse

Author

Listed:
  • Ji Chen

    (East China Normal University)

  • Jun Shao

    (East China Normal University
    University of Wisconsin-Madison)

  • Fang Fang

    (East China Normal University)

Abstract

With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector called instrument that can be excluded from the nonresponse propensity, but are associated with the response even when other covariates are conditioned. The existing work in this approach assumes such an instrument is given, which is frequently not the case in applications. In this paper, we investigate how to search for an instrument from a given set of covariates, based on a pseudo likelihood approach assuming a parametric distribution of response conditioned on covariates and a totally unspecified nonresponse propensity. We propose a method and show that it produces a consistent instrument selection as the sample size tends to infinity, under some regularity conditions. The proposed method is examined in a simulation study and illustrated in a real data example.

Suggested Citation

  • Ji Chen & Jun Shao & Fang Fang, 2021. "Instrument search in pseudo-likelihood approach for nonignorable nonresponse," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 519-533, June.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:3:d:10.1007_s10463-020-00758-z
    DOI: 10.1007/s10463-020-00758-z
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    References listed on IDEAS

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    1. 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.
    2. Wang Miao & Peng Ding & Zhi Geng, 2016. "Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1673-1683, October.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. repec:mpr:mprres:8160 is not listed on IDEAS
    5. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    6. 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.
    7. 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.
    8. Ji Chen & Bingying Xie & Jun Shao, 2018. "Pseudo likelihood and dimension reduction for data with nonignorable nonresponse," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 2(2), pages 196-205, July.
    9. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
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    Cited by:

    1. Zhao, Yujie & Huo, Xiaoming, 2023. "Accelerate the warm-up stage in the Lasso computation via a homotopic approach," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).

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