A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean

Bonface Miya Malenje; Winnie Onsongo Mokeira; Romanus Odhiambo; George Otieno Orwa

doi:doi:10.11648/j.ajtas.20160505.21

| Peer-Reviewed

A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean

Bonface Miya Malenje, Winnie Onsongo Mokeira, Romanus Odhiambo, George Otieno Orwa

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

Received: 28 September 2015 Accepted: 20 October 2015 Published: 28 September 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.21
Page(s)	317-325
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

Multiplicative Bias, Nonparametric Model, Finite Population Mean, Conditional Bias

References

[1]	A. H. Dorfman. (1992). Nonparametric regression for estimating totals in finite pop- ulations, proceedings of the section on survey research methods. American Statistical Association, 1992, pp. 622-625.
[2]	Breidt, F. J., & Opsomer, J. D. (2000, 08). Local polynomial regression estimators in survey sampling. Ann. Statist., 28 (4), 1026– 1053.
[3]	Chambers, R., & Dorfman, A. (2003). Robust sample survey inference via boot- strapping and bias correction: The case of the ratio estimator.
[4]	Chambers, R. L., Dorfman, A. H., & Wehrly, T. E. (1993). Bias robust estimation in finite populations using nonparametric calibration. Journal of the American Statistical Association, 88 (421), 268-277. Cochran, W. G. (2007). Sampling techniques. John Wiley & Sons.
[5]	Efron, B. (1982). the jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics.
[6]	Fan, J., & Gijbels, I. (1992, 12).Variable bandwidth and local linear regression smoothers Ann. Statist., 20 (4), 2008–2036.
[7]	Gasser, T., & Müller, H.-G. (1979). Kernel estimation of regression functions.
[8]	Godambe, V. (1955). A unified theory of sampling from finite populations. Journal of the Royal Statistical Society. Series B (Methodological), 269–278.
[9]	Hengartner, N., Matzner-Lober, E., Rouviere, L., & Burr, T. (2009). Multiplicative bias corrected nonparametric smoothers.
[10]	Kwong-Aquino, A. A. H. (2011). Nonparametric model-based predictive estimation in survey sampling. The Philippine Statistician.
[11]	Linton, O., & Nielsen, J. P. (1994). A multiplicative bias reduction method for nonparametric regression. Statistics & Probability Letters, 19 (3), 181–187.
[12]	Onyango, C. O., Otieno, R. O., & Orwa, G. O. (2010). Generalised model based confidence intervals in two stage cluster sampling. Pakistan Journal of Statistics and Operation Research, 6 (2), 101–115.
[13]	Ouma, C., & Wafula, C. (2007). Bootstrap confidence intervals for model-based surveys. East African Journal of Statistics, 1 (1), 84–90.
[14]	Pensky, M., Vidakovic, B., et al. (1999). Adaptive wavelet estimator for nonparametric density deconvolution. The Annals of Statistics, 27 (6), 2033–2053.
[15]	Priestley, M., & Chao, M. (1972). Non-parametric function fitting. Journal of the Royal Statistical Society. Series B (Methodological), 385–392.
[16]	Rao, J. N., & Wu, C. (1988). Resampling inference with complex survey data.
[17]	Rueda, M., & Sánchez-Borrego, I. (2009). A predictive estimator of finite population mean using nonparametric regression. Computational Statistics, 24 (1), 1–14.
[18]	Zheng, H., & Little, R. (2004). Inference for the population total from probability-proportional-to-size samples based on predictions from a penalized spline non- parametric model. Journal of Official statistics.
[19]	Zheng, H., & Little, R. J. (2003). Penalized spline model-based estimation of the finite populations total from probability-proportional-to-size samples. Journal of offi statistics-Stockholm-, 19 (2), 99–118.

Cite This Article

Plain Text BibTeX RIS

APA Style

Bonface Miya Malenje, Winnie Onsongo Mokeira, Romanus Odhiambo, George Otieno Orwa. (2016). A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. American Journal of Theoretical and Applied Statistics, 5(5), 317-325. https://doi.org/10.11648/j.ajtas.20160505.21

Copy | Download

ACS Style

Bonface Miya Malenje; Winnie Onsongo Mokeira; Romanus Odhiambo; George Otieno Orwa. A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. Am. J. Theor. Appl. Stat. 2016, 5(5), 317-325. doi: 10.11648/j.ajtas.20160505.21

Copy | Download

AMA Style

Bonface Miya Malenje, Winnie Onsongo Mokeira, Romanus Odhiambo, George Otieno Orwa. A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. Am J Theor Appl Stat. 2016;5(5):317-325. doi: 10.11648/j.ajtas.20160505.21

Copy | Download

@article{10.11648/j.ajtas.20160505.21,
  author = {Bonface Miya Malenje and Winnie Onsongo Mokeira and Romanus Odhiambo and George Otieno Orwa},
  title = {A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {317-325},
  doi = {10.11648/j.ajtas.20160505.21},
  url = {https://doi.org/10.11648/j.ajtas.20160505.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.21},
  abstract = {Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean
AU  - Bonface Miya Malenje
AU  - Winnie Onsongo Mokeira
AU  - Romanus Odhiambo
AU  - George Otieno Orwa
Y1  - 2016/09/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.21
DO  - 10.11648/j.ajtas.20160505.21
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  - 317
EP  - 325
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.21
AB  - Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.
VL  - 5
IS  - 5
ER  -

Copy | Download

Author Information

Bonface Miya Malenje

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Winnie Onsongo Mokeira

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Romanus Odhiambo

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
George Otieno Orwa

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Bonface Miya Malenje, Winnie Onsongo Mokeira, Romanus Odhiambo, George Otieno Orwa. (2016). A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. American Journal of Theoretical and Applied Statistics, 5(5), 317-325. https://doi.org/10.11648/j.ajtas.20160505.21

Copy | Download

ACS Style

Bonface Miya Malenje; Winnie Onsongo Mokeira; Romanus Odhiambo; George Otieno Orwa. A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. Am. J. Theor. Appl. Stat. 2016, 5(5), 317-325. doi: 10.11648/j.ajtas.20160505.21

Copy | Download

AMA Style

Bonface Miya Malenje, Winnie Onsongo Mokeira, Romanus Odhiambo, George Otieno Orwa. A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean. Am J Theor Appl Stat. 2016;5(5):317-325. doi: 10.11648/j.ajtas.20160505.21

Copy | Download

@article{10.11648/j.ajtas.20160505.21,
  author = {Bonface Miya Malenje and Winnie Onsongo Mokeira and Romanus Odhiambo and George Otieno Orwa},
  title = {A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {317-325},
  doi = {10.11648/j.ajtas.20160505.21},
  url = {https://doi.org/10.11648/j.ajtas.20160505.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.21},
  abstract = {Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean
AU  - Bonface Miya Malenje
AU  - Winnie Onsongo Mokeira
AU  - Romanus Odhiambo
AU  - George Otieno Orwa
Y1  - 2016/09/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.21
DO  - 10.11648/j.ajtas.20160505.21
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  - 317
EP  - 325
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.21
AB  - Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.
VL  - 5
IS  - 5
ER  -

Copy | Download