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Empirical likelihood-based hot deck imputation methods

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  • Yijie Xue
  • Nicole Lazar

Abstract

The non-response problem commonly exists in survey data and has been investigated by various methods. We propose an empirical likelihood-based hot deck imputation method, which resamples the observed data by using the weights from the empirical likelihood ratio for missing values. We demonstrate that the estimator of the mean is unbiased and the corresponding variance estimator of the mean is asymptotically unbiased under mild conditions. Next, we extend our method for U-statistic estimators and show that the estimator converges to the real U-statistic in probability. The proposed method can also incorporate multiple imputations and/or regression imputations easily. Simulations and a real example illustrate that our method outperforms some of the existing approaches, such as simple hot deck imputation and fractional hot deck imputation. We conclude with a discussion of the advantages of the empirical likelihood-based hot deck imputation method.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:629-646
    DOI: 10.1080/10485252.2012.690879
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    References listed on IDEAS

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    1. Jae Kwang Kim, 2011. "Parametric fractional imputation for missing data analysis," Biometrika, Biometrika Trust, vol. 98(1), pages 119-132.
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    3. Jae Kwang Kim, 2004. "Fractional hot deck imputation," Biometrika, Biometrika Trust, vol. 91(3), pages 559-578, September.
    4. Grendar, Marian & Judge, George G, 2009. "Maximum Empirical Likelihood: Empty Set Problem," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt71v338mh, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Qin, Jing & Shao, Jun & Zhang, Biao, 2008. "Efficient and Doubly Robust Imputation for Covariate-Dependent Missing Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 797-810, June.
    6. Rebecca R. Andridge & Roderick J. A. Little, 2010. "A Review of Hot Deck Imputation for Survey Non‐response," International Statistical Review, International Statistical Institute, vol. 78(1), pages 40-64, April.
    7. Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
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