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Estimation in semiparametric models with missing data

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  • Chen, Song Xi
  • Van Keilegom, Ingrid

Abstract

This paper considers the problem of parameter estimation in a general class of semiparametric models when observations are subject to missingness at random. The semiparametric models allow for estimating functions that are non-smooth with respect to the parameter. We propose a nonparametric imputation method for the missing values, which then leads to imputed estimating equations for the finite dimensional parameter of interest. The asymptotic normality of the parameter estimator is proved in a general setting, and is investigated in detail for a number of specific semiparametric models. Finally, we study the small sample performance of the proposed estimator via simulations. Copyright The Institute of Statistical Mathematics, Tokyo 2013
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Suggested Citation

  • Chen, Song Xi & Van Keilegom, Ingrid, 2013. "Estimation in semiparametric models with missing data," LIDAM Reprints ISBA 2013024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2013024
    Note: In : Annals of the Institute of Statistical Mathematics, vol. 65, no. 4, p. 785-805 (2013)
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    1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
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    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. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
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    10. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, January.
    11. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    12. Chen, Qingxia & Zeng, Donglin & Ibrahim, Joseph G., 2007. "Sieve Maximum Likelihood Estimation for Regression Models With Covariates Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1309-1317, December.
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    Cited by:

    1. Ana M. Bianco & Graciela Boente & Wenceslao González-Manteiga & Ana Pérez-González, 2019. "Plug-in marginal estimation under a general regression model with missing responses and covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 106-146, March.
    2. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    3. 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.
    4. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.

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