Non-parametric Variance Estimation Using Donor Imputation Method

Hellen W. Waititu; Edward Njenga

doi:doi:10.11648/j.ajtas.20160505.11

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Non-parametric Variance Estimation Using Donor Imputation Method

Hellen W. Waititu, Edward Njenga

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

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.

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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
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.11
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

Hellen W. Waititu

Department of Statistics and Computer Sciences, Moi University, Nairobi, Kenya
Edward Njenga

Department of Mathematics, Kenyatta University, Nairobi, Kenya

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Non-parametric Variance Estimation Using Donor Imputation Method
AU  - Hellen W. Waititu
AU  - Edward Njenga
Y1  - 2016/08/03
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.11
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  -

Copy | Download