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Local multiple imputation

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  • Marc Aerts

Abstract

Dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships. If such parametric assumptions do not hold, the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results. In this paper, a fully nonparametric and a semiparametric imputation method are studied, both based on local resampling principles. It is shown that the final estimator, based on these local imputations, is consistent under fewer or no parametric assumptions. Asymptotic expressions for bias, variance and mean squared error are derived, showing the theoretical impact of the different smoothing parameters. Simulations illustrate the usefulness and applicability of the method. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:375-388
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    Citations

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    Cited by:

    1. Yijie Xue & Nicole Lazar, 2012. "Empirical likelihood-based hot deck imputation methods," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 629-646.
    2. Bianco, Ana & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2010. "Estimation of the marginal location under a partially linear model with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 546-564, February.
    3. Huang, Ming-Yueh & Chan, Kwun Chuen Gary, 2018. "Joint sufficient dimension reduction for estimating continuous treatment effect functions," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 48-62.
    4. Nicklas Pettersson, 2013. "Bias reduction of finite population imputation by kernel methods," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 14(1), pages 139-160, March.
    5. 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.
    6. Qiu, Zhiping & Chen, Xiaoping & Zhou, Yong, 2015. "A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 89-97.
    7. Shuanghua Luo & Changlin Mei & Cheng-yi Zhang, 2017. "Smoothed empirical likelihood for quantile regression models with response data missing at random," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 95-116, January.
    8. Peisong Han, 2016. "Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 246-260, March.
    9. Xuerong Chen & Alan T. K. Wan & Yong Zhou, 2015. "Efficient Quantile Regression Analysis With Missing Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 723-741, June.
    10. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.

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