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Doubly Robust Estimation and Semiparametric Efficiency in Generalized Partially Linear Models with Missing Outcomes

Author

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  • Lu Wang

    (Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA)

  • Zhongzhe Ouyang

    (Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA)

  • Xihong Lin

    (Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA)

Abstract

We investigate a semiparametric generalized partially linear regression model that accommodates missing outcomes, with some covariates modeled parametrically and others nonparametrically. We propose a class of augmented inverse probability weighted (AIPW) kernel–profile estimating equations. The nonparametric component is estimated using AIPW kernel estimating equations, while parametric regression coefficients are estimated using AIPW profile estimating equations. We demonstrate the doubly robust nature of the AIPW estimators for both nonparametric and parametric components. Specifically, these estimators remain consistent if either the assumed model for the probability of missing data or that for the conditional mean of the outcome, given covariates and auxiliary variables, is correctly specified, though not necessarily both simultaneously. Additionally, the AIPW profile estimator for parametric regression coefficients is consistent and asymptotically normal under the semiparametric model defined by the generalized partially linear model on complete data, assuming that the missing data mechanism is missing at random. When both working models are correctly specified, this estimator achieves semiparametric efficiency, with its asymptotic variance reaching the efficiency bound. We validate our approach through simulations to assess the finite sample performance of the proposed estimators and apply the method to a study that investigates risk factors associated with myocardial ischemia.

Suggested Citation

  • Lu Wang & Zhongzhe Ouyang & Xihong Lin, 2024. "Doubly Robust Estimation and Semiparametric Efficiency in Generalized Partially Linear Models with Missing Outcomes," Stats, MDPI, vol. 7(3), pages 1-20, August.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:3:p:56-943:d:1468558
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    References listed on IDEAS

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    1. Tao Hu & Hengjian Cui, 2010. "Robust estimates in generalised varying-coefficient partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 737-754.
    2. Song Chen & Ingrid Van Keilegom, 2013. "Estimation in semiparametric models with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 785-805, August.
    3. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    4. Qi-Hua Wang, 2009. "Statistical estimation in partial linear models with covariate data missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 47-84, March.
    5. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    6. Rotnitzky, Andrea & Holcroft, Christina A. & Robins, James M., 1997. "Efficiency Comparisons in Multivariate Multiple Regression with Missing Outcomes," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 102-128, April.
    7. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    8. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    9. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    10. Jafer Rahman & Shihua Luo & Yawen Fan & Xiaohui Liu, 2020. "Semiparametric efficient inferences for generalised partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 704-724, July.
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