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Non-parametric Variance Estimation Using Donor Imputation Method

Received: 1 July 2016     Accepted: 16 July 2016     Published: 3 August 2016
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Abstract

The main objective of this study is to investigate the relative performance of donor imputation method in situations that are likely to occur in practice and to carry out numerical comparative study of estimators of variance using Nadaraya-Watson kernel estimators and other estimators. Nadaraya-Watson kernel estimator can be viewed as a non-parametric imputation method as it leads to an imputed estimator with negligible bias without requiring the specification of a parametric imputation model. Simulation studies were carried out to investigate the performance of Nadaraya-Watson kernel estimators in terms of variance. From the results, it was found out that Nadaraya-Watson kernel estimator has negligible bias and its variance is small. When compared with Naïve, Jackknife and Bootstrap estimators, Nadaraya-Watson kernel estimator was found to perform better than bootstrap estimator in linear and non-linear populations.

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI 10.11648/j.ajtas.20160505.11
Page(s) 252-259
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Hot Deck Imputation, Non-parametric, Unbiased Estimator, Donor, Recipient, Donor Imputation

References
[1] Beaumont, J. F. and Bocci, C. (2009). Variance estimation when donor imputation is used to fill in missing values. Canadian Journal of Statistics, 96 (4), 917-932.
[2] Beaumont, J. F. and Bocci, C. (2007). Variance estimation when donor imputation is used to fill in missing values. Proceedings of the Third International Conference on Establishment Surveys, Montréal.
[3] F. W. Scholz (2007). The Bootstrap Small Sample Properties. University of Washington
[4] Brick, J. M., Kalton, G. and Kim, J. K. (2004). Variance estimation with hot deck imputation using a model. Survey Methodology, 30, 57-66.
[5] Chen, J. and Shao, J. (2000). Nearest neighbour imputation for survey data. Journal of Official Statistics, 16, 113–131.
[6] Chen, J. and Shao, J. (2001). Jackknife variance estimation for nearest neighbor imputation. Journal of the American statistics Association, 96, 260-269.
[7] Fuller, A. and Kim, J. K. (2000). Hot Deck Imputation for the Response Model. Vol. 31, No. 2, pp. 139-149 Statistics Canada, Catalogue No. 12-00 Statistica Sinica 10, 1153-1169.
[8] Jae Kwang Kim (2001). Variance Estimation After Imputation. Statistics Canada, Catalogue No. 12001Vol. 27, No. 1, pp. 7583
[9] Njenga, E. G. (1990). Robust estimation of the regression coefficients in complex surveys. (Doctoral dissertation, 1990).
[10] Rao, J. N. K. and Shao, J. (1992). Jackknife Variance Estimation with Survey Data under Hot Deck Imputation. Biometrika, 79, 811-822.
[11] Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. John Wiley & Sons, New York.
[12] Shao, J., and Steel, P. (1999). Variance estimation for survey data with composite imputation and nonnegligible sampling fractions. Journal of the American Statistical Association, 94, 254-265.
[13] Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap. New York: Springer-Verlag.
Cite This Article
  • APA Style

    Hellen W. Waititu, Edward Njenga. (2016). Non-parametric Variance Estimation Using Donor Imputation Method. American Journal of Theoretical and Applied Statistics, 5(5), 252-259. https://doi.org/10.11648/j.ajtas.20160505.11

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    ACS Style

    Hellen W. Waititu; Edward Njenga. Non-parametric Variance Estimation Using Donor Imputation Method. Am. J. Theor. Appl. Stat. 2016, 5(5), 252-259. doi: 10.11648/j.ajtas.20160505.11

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    AMA Style

    Hellen W. Waititu, Edward Njenga. Non-parametric Variance Estimation Using Donor Imputation Method. Am J Theor Appl Stat. 2016;5(5):252-259. doi: 10.11648/j.ajtas.20160505.11

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  • @article{10.11648/j.ajtas.20160505.11,
      author = {Hellen W. Waititu and Edward Njenga},
      title = {Non-parametric Variance Estimation Using Donor Imputation Method},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {5},
      number = {5},
      pages = {252-259},
      doi = {10.11648/j.ajtas.20160505.11},
      url = {https://doi.org/10.11648/j.ajtas.20160505.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.11},
      abstract = {The main objective of this study is to investigate the relative performance of donor imputation method in situations that are likely to occur in practice and to carry out numerical comparative study of estimators of variance using Nadaraya-Watson kernel estimators and other estimators. Nadaraya-Watson kernel estimator can be viewed as a non-parametric imputation method as it leads to an imputed estimator with negligible bias without requiring the specification of a parametric imputation model. Simulation studies were carried out to investigate the performance of Nadaraya-Watson kernel estimators in terms of variance. From the results, it was found out that Nadaraya-Watson kernel estimator has negligible bias and its variance is small. When compared with Naïve, Jackknife and Bootstrap estimators, Nadaraya-Watson kernel estimator was found to perform better than bootstrap estimator in linear and non-linear populations.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Non-parametric Variance Estimation Using Donor Imputation Method
    AU  - Hellen W. Waititu
    AU  - Edward Njenga
    Y1  - 2016/08/03
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    DO  - 10.11648/j.ajtas.20160505.11
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 252
    EP  - 259
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20160505.11
    AB  - The main objective of this study is to investigate the relative performance of donor imputation method in situations that are likely to occur in practice and to carry out numerical comparative study of estimators of variance using Nadaraya-Watson kernel estimators and other estimators. Nadaraya-Watson kernel estimator can be viewed as a non-parametric imputation method as it leads to an imputed estimator with negligible bias without requiring the specification of a parametric imputation model. Simulation studies were carried out to investigate the performance of Nadaraya-Watson kernel estimators in terms of variance. From the results, it was found out that Nadaraya-Watson kernel estimator has negligible bias and its variance is small. When compared with Naïve, Jackknife and Bootstrap estimators, Nadaraya-Watson kernel estimator was found to perform better than bootstrap estimator in linear and non-linear populations.
    VL  - 5
    IS  - 5
    ER  - 

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Author Information
  • Department of Statistics and Computer Sciences, Moi University, Nairobi, Kenya

  • Department of Mathematics, Kenyatta University, Nairobi, Kenya

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