Semiparametric inference for estimating equations with nonignorably missing covariates

References

• Bashir, S.A., and Duffy, S.W. (1997), ‘The Correction of Risk Estimates for Measurement Error’, Annals of Epidemiology, 7, 154–164. doi: 10.1016/S1047-2797(96)00149-4
   PubMed Web of Science ®Google Scholar
• Chen, S.X. (2013), ‘A Unified Theory on Empirical Likelihood Methods for Missing Data’, Statistics and its Interface, 6, 325–338. doi: 10.4310/SII.2013.v6.n3.a3
   Web of Science ®Google Scholar
• Chen, X.H., Hong, H., and Tarozzi, A. (2008), ‘Semiparametric Efficiency in GMM Models with Auxiliary Data’, The Annals of Statistics, 36, 808–843. doi: 10.1214/009053607000000947
   Web of Science ®Google Scholar
• Fang, F., and Shao, J. (2016), ‘Model Selection with Nonignorable Nonresponse’, Biometrika, 103, 861–874. doi: 10.1093/biomet/asw039
   Web of Science ®Google Scholar
• Fang, F., Zhao, J., and Shao, J. (2018), ‘Imputation-based Adjusted Score Equations in Generalized Linear Models with Nonignorable Missing Covariate Values’, Statistica Sinica, In press.
   Google Scholar
• Godambe, V.P. (1991), Estimating Functions, Oxford, UK: Oxford University Press.
   Google Scholar
• Hansen, L.P. (1982), ‘Large Sample Properties of Generalized Method of Moments Estimators’, Econometrica, 50, 1029–1054. doi: 10.2307/1912775
   Web of Science ®Google Scholar
• Hardin, J.W., and Hilbe, J.M. (2003), Generalized Estimating Equations, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Hjort, N.L., McKeague, I.W., and Keilegom, I.V. (2009), ‘Extending the Scope of Empirical Likelihood’, The Annals of Statistics, 37, 1079–1111. doi: 10.1214/07-AOS555
   Web of Science ®Google Scholar
• Horton, N.J., and Laird, N.M. (2001), ‘Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information’, Biometrics, 57, 34–42. doi: 10.1111/j.0006-341X.2001.00034.x
   PubMed Web of Science ®Google Scholar
• Ibrahim, J.G., Chen, M.-H., and Lipsitz, S.R. (1999), ‘Monte Carlo EM for Missing Covariates in Parametric Regression Models’, Biometrics, 55, 591–596. doi: 10.1111/j.0006-341X.1999.00591.x
   PubMed Web of Science ®Google Scholar
• Kim, J.K., and Yu, C.L. (2011), ‘A Semiparametric Estimation of Mean Functionals with Nonignorable Missing Data’, Journal of the American Statistical Association, 106, 157–165. doi: 10.1198/jasa.2011.tm10104
   Web of Science ®Google Scholar
• Liang, K.Y., and Zeger, S.L. (1995), ‘Inference Based on Estimating Functions in the Presence of Nuisance Parameters (with discussion)’, Statistical Science, 10, 158–173. doi: 10.1214/ss/1177010028
   Web of Science ®Google Scholar
• Lipsitz, S.R., Ibrahim, J.G., Chen, M. -H., and Peterson, H. (1999), ‘Nonignorable Missing Covariates in Generalized Linear Models’, Statistics in Medicine, 18, 2435–2448. doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2435::AID-SIM267>3.0.CO;2-B
   PubMed Web of Science ®Google Scholar
• Little, R.J., and Rubin, D.B. (2002), Statistical Analysis with Missing Data (2nd ed.), New York: Wiley.
   Google Scholar
• Miao, W., and Tchetgen Tchetgen, E. (2018), ‘Identification and Inference with Nonignorable Missing Covariate Data’, Statistica Sinica, In press.
   Google Scholar
• Owen, A. (1990), ‘Empirical Likelihood Ratio Confidence Regions’, The Annals of Statistics, 18, 90–120. doi: 10.1214/aos/1176347494
   Web of Science ®Google Scholar
• Owen, A.B. (2001), Empirical Likelihood, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Qin, J., and Lawless, J. (1994), ‘Empirical Likelihood and General Estimating Equations’, The Annals of Statistics, 22, 300–325. doi: 10.1214/aos/1176325370
   Web of Science ®Google Scholar
• Qin, J., Leung, D., and Shao, J. (2002), ‘Estimation with Survey Data Under Nonignorable Nonresponse or Informative Sampling’, Journal of the American Statistical Association, 97, 193–200. doi: 10.1198/016214502753479338
   Web of Science ®Google Scholar
• Reilly, M., and Pepe, M.S. (1995), ‘A Mean Score Method for Missing and Auxiliary Covariate Data in Regression Models’, Biometrika, 82, 299–314. doi: 10.1093/biomet/82.2.299
   Web of Science ®Google Scholar
• Robins, J.M., and Ritov, Y. (1997), ‘Toward a Curse of Dimensionality Appropriate (CODA) Asymptotic Theory for Semi-parametric Models’, Statistics in Medicine, 16, 285–319. doi: 10.1002/(SICI)1097-0258(19970215)16:3<285::AID-SIM535>3.0.CO;2-#
   PubMed Web of Science ®Google Scholar
• Robins, J.M., Rotnitzky, A., and Zhao, L.P. (1994), ‘Estimation of Regression Coefficients When Some Regressors are not Always Observed’, Journal of the American Statistical Association, 89, 846–866. doi: 10.1080/01621459.1994.10476818
   Web of Science ®Google Scholar
• Robins, J.M., Rotnitzky, A., and Zhao, L.P. (1995), ‘Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data’, Journal of the American Statistical Association, 90, 106–121. doi: 10.1080/01621459.1995.10476493
   Web of Science ®Google Scholar
• Rotnitzky, A., and Robins, J.M. (1997), ‘Analysis of Semiparametric Regression Models with Nonignorable Nonresponse’, Statistics in Medicine, 16, 81–102. doi: 10.1002/(SICI)1097-0258(19970115)16:1<81::AID-SIM473>3.0.CO;2-0
   PubMed Web of Science ®Google Scholar
• Shao, J., and Wang, L. (2016), ‘Semiparametric Inverse Propensity Weighting for Nonignorable Missing Data’, Biometrika, 103, 175–187. doi: 10.1093/biomet/asv071
   Web of Science ®Google Scholar
• Shao, J., and Zhao, J.W. (2013), ‘Estimation in Longitudinal Studies with Nonignorable Dropout’, Statistics and its Interface, 6, 303–313. doi: 10.4310/SII.2013.v6.n3.a1
   Web of Science ®Google Scholar
• Tang, C.Y., and Qin, Y.S. (2012), ‘An Efficient Empirical Likelihood Approach for Estimating Equations with Missing Data’, Biometrika, 99, 1001–1007. doi: 10.1093/biomet/ass045
   Web of Science ®Google Scholar
• Tang, G., Little, R.J.A., and Raghunathan, T.E. (2003), ‘Analysis of Multivariate Missing Data with Nonignorable Nonresponse’, Biometrika, 90, 747–764. doi: 10.1093/biomet/90.4.747
   Web of Science ®Google Scholar
• Tang, N.S., Zhao, P.Y., and Zhu, H.T. (2014), ‘Empirical Likelihood for Estimating Equations with Nonignorably Missing Data’, Statistica Sinica, 24, 723–748.
   PubMed Web of Science ®Google Scholar
• Troxel, A.B., Lipsitz, S.R., and Brennan, T.A. (1997), ‘Weighted Estimating Equations with Nonignorably Missing Response Data’, Biometrics, 53, 857–869. doi: 10.2307/2533548
   PubMed Web of Science ®Google Scholar
• Wang, D., and Chen, S.X. (2009), ‘Empirical Likelihood for Estimating Equations with Missing Values’, The Annals of Statistics, 37, 490–517. doi: 10.1214/07-AOS585
   Web of Science ®Google Scholar
• Wang, S., Shao, J., and Kim, J.K. (2014), ‘An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse’, Statistica Sinica, 24, 1097–1116.
   Web of Science ®Google Scholar
• Wang, X.L., Chen, F., and Lin, L. (2013), ‘Empirical Likelihood Inference for Estimating Equation with Missing Data’, Science China Mathematics, 56, 1233–1245. doi: 10.1007/s11425-012-4504-x
   Web of Science ®Google Scholar
• Wang, Y.G. (1999), ‘Estimating Equations with Nonignorably Missing Response Data’, Biometrics, 55, 984–989. doi: 10.1111/j.0006-341X.1999.00984.x
   PubMed Web of Science ®Google Scholar
• Wei, G.C., and Tanner, M.A. (1990), ‘A Monte Carlo Implementation of the EM Algorithm and the Poor Mans Data Augmentation Algorithms’, Journal of the American Statistical Association, 85, 699–704. doi: 10.1080/01621459.1990.10474930
   Web of Science ®Google Scholar
• Zhao, J. (2017), ‘Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism’, Journal of Nonparametric Statistics, 29, 577–593. doi: 10.1080/10485252.2017.1339306
   PubMed Web of Science ®Google Scholar
• Zhao, J., and Shao, J. (2015), ‘Semiparametric Pseudo Likelihoods in Generalized Linear Models with Nonignorable Missing Data’, Journal of the American Statistical Association, 110, 1577–1590. doi: 10.1080/01621459.2014.983234
   Web of Science ®Google Scholar
• Zhao, J., and Shao, J. (2017), ‘Approximate Conditional Likelihood for Generalized Liner Models with General Missing Data Mechanism’, Journal of Systems Science and Complexity, 30, 139–153. doi: 10.1007/s11424-017-6188-3
   Web of Science ®Google Scholar
• Zhao, J., Yang, Y., and Ning, Y., (2018), ‘Penalized Pairwise Pseudo Likelihood for Variable Selection with Nonignorable Missing Data’, Statistica Sinica, In press.
   Google Scholar
• Zhao, P.Y., Tang, N.S., Qu, A., and Jiang, D.P. (2017), ‘Semiparametric Estimating Equations Inference with Nonignorable Missing Data’, Statistica Sinica, 27, 89–113.
   Web of Science ®Google Scholar
• Zhou, Y., Wan, A.T.K, and Wang, X. (2008), ‘Estimating Equations Inference with Missing Data’, Journal of the American Statistical Association, 103, 1187–1199. doi: 10.1198/016214508000000535
   Web of Science ®Google Scholar