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Estimation in semiparametric models with missing data

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  • Song Chen
  • Ingrid Van Keilegom

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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  • 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.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:785-805
    DOI: 10.1007/s10463-012-0393-6
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    1. 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.
    2. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    3. 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.
    4. 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.

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