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Estimation with multivariate outcomes having nonignorable item nonresponse

Author

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  • Lyu Ni

    (East China Normal University)

  • Jun Shao

    (East China Normal University
    East China Normal University)

Abstract

To estimate unknown population parameters based on $${\varvec{y}}$$ y , a vector of multivariate outcomes having nonignorable item nonresponse that directly depends on $${\varvec{y}}$$ y , we propose an innovative inverse propensity weighting approach when the joint distribution of $${\varvec{y}}$$ y and associated covariate $${\varvec{x}}$$ x is nonparametric and the nonresponse probability conditional on $${\varvec{y}}$$ y and $${\varvec{x}}$$ x has a parametric form. To deal with the identifiability issue, we utilize a nonresponse instrument $${\varvec{z}}$$ z , an auxiliary variable related to $${\varvec{y}}$$ y but not related to the nonresponse probability conditional on $${\varvec{y}}$$ y and $${\varvec{x}}$$ x . We utilize a modified generalized method of moments to obtain estimators of the parameters in the nonresponse probability. Simulation results are presented and an application is illustrated in a real data set.

Suggested Citation

  • Lyu Ni & Jun Shao, 2023. "Estimation with multivariate outcomes having nonignorable item nonresponse," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 1-15, February.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:1:d:10.1007_s10463-022-00836-4
    DOI: 10.1007/s10463-022-00836-4
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. repec:mpr:mprres:8160 is not listed on IDEAS
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    4. Jun Shao & Lei Wang, 2016. "Semiparametric inverse propensity weighting for nonignorable missing data," Biometrika, Biometrika Trust, vol. 103(1), pages 175-187.
    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. Lei Xu & Jun Shao, 2009. "Estimation in Longitudinal or Panel Data Models with Random-Effect-Based Missing Responses," Biometrics, The International Biometric Society, vol. 65(4), pages 1175-1183, December.
    8. Sijing Li & Jun Shao, 2022. "Nonignorable item nonresponse in panel data," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 6(1), pages 58-71, January.
    9. J. Shao & J. Zhang, 2015. "A transformation approach in linear mixed-effects models with informative missing responses," Biometrika, Biometrika Trust, vol. 102(1), pages 107-119.
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