On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys

Conlet Biketi Kikechi; Richard Onyino Simwa; Ganesh Prasad Pokhariyal

doi:doi:10.11648/j.ajtas.20180703.11

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On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys

Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 3)

Received: 10 February 2018 Accepted: 6 March 2018 Published: 24 March 2018

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Abstract

In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 3)
DOI	10.11648/j.ajtas.20180703.11
Page(s)	92-101
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), 2018. Published by Science Publishing Group

Keywords

Nonparametric Regression, Finite Population Totals, Local Linear Regression, Robustness Properties, Confidence Intervals, Model Based Surveys

References

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[4]	A. Kuk, "A Kernel method for estimating finite population distribution functions using auxiliary information," Biometrika, vol. Vol 80, pp. 385-392, (1993).
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[6]	A. H. Dorfman, "Non-Parametric Regression for Estimating Totals in Finite populations, Proceedings of the Section on Survey Research Method.," American Statistical Association, pp. 622-625, (1992).
[7]	C. B. Kikechi, R. O. Simwa and G. P. Pokhariyal, "On Local Linear Regression Estimation in Sampling Surveys," Far east Journal of Theoretical Statistics,, vol. 53, no. 5, pp. 291-311, (2017).
[8]	R. L. Chambers, A. H. Dorfman and T. E. Wehrly, "Bias robust estimation in finite populations using nonparametric calibration," J. Amer Statist Assoc., Vols. 88,, pp. 268-277, (1993).
[9]	R. L. Chambers and A. H. Dorfman, "Nonparametric regression with complex survey data," Survey Methods Research Bureau of Labor Statistics, (2002).
[10]	J. Fan and I. Gijbels, Local Polynomial Modeling and its Applications, London: Chapman and Hall, (1996).
[11]	H. Zheng and R. J. Little, "Penalized Spline Model-Based Estimation of the Finite Population Total from Probability-Proportional-To-Size Samples," Journal of official Statistics, vol. 19, p. 99–117, (2003).
[12]	H. Zheng and R. J. Little, "Penalized Spline Nonparametric Mixed Models for Inference about a Finite Population Mean from Two-Stage Samples," Survey Methodology, vol. 30, pp. 209-218, (2004).
[13]	F. J. Breidt and J. D. Opsomer, "Local Polynomial Regression Estimation in Survey Sampling," Annals of Statistics, vol. 28, pp. 1026-1053, (2000).
[14]	B. I. Sanchez, J. D. Opsomer, M. Rueda and A. Arcos, "Non-parametric Estimation with mixed data types in survey sampling," Rev Mat complut,, vol. 27, pp. 685-700, (2014).
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[16]	D. Ruppert and M. P. Wand, "Multivariate locally weighted least squares regression," Annals of Statistics, vol. 22, p. 1346–1370, (1994).
[17]	J. Fan, "Local linear regression smoothers and their minimax efficiencies," Annals of Statistics, vol. 21, p. 196–216, (1993).
[18]	B. Silverman, "Density Estimation for Statistics and Data Analysis," in Monographs on Statistics and Applied Probability, London, Chapman and Hall, (1986).

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APA Style

Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal. (2018). On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. American Journal of Theoretical and Applied Statistics, 7(3), 92-101. https://doi.org/10.11648/j.ajtas.20180703.11

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ACS Style

Conlet Biketi Kikechi; Richard Onyino Simwa; Ganesh Prasad Pokhariyal. On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. Am. J. Theor. Appl. Stat. 2018, 7(3), 92-101. doi: 10.11648/j.ajtas.20180703.11

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AMA Style

Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal. On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. Am J Theor Appl Stat. 2018;7(3):92-101. doi: 10.11648/j.ajtas.20180703.11

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@article{10.11648/j.ajtas.20180703.11,
  author = {Conlet Biketi Kikechi and Richard Onyino Simwa and Ganesh Prasad Pokhariyal},
  title = {On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {3},
  pages = {92-101},
  doi = {10.11648/j.ajtas.20180703.11},
  url = {https://doi.org/10.11648/j.ajtas.20180703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180703.11},
  abstract = {In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.},
 year = {2018}
}

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TY  - JOUR
T1  - On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys
AU  - Conlet Biketi Kikechi
AU  - Richard Onyino Simwa
AU  - Ganesh Prasad Pokhariyal
Y1  - 2018/03/24
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180703.11
DO  - 10.11648/j.ajtas.20180703.11
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  - 92
EP  - 101
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180703.11
AB  - In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.
VL  - 7
IS  - 3
ER  -

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Author Information

Conlet Biketi Kikechi

School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Richard Onyino Simwa

School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Ganesh Prasad Pokhariyal

School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal. (2018). On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. American Journal of Theoretical and Applied Statistics, 7(3), 92-101. https://doi.org/10.11648/j.ajtas.20180703.11

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ACS Style

Conlet Biketi Kikechi; Richard Onyino Simwa; Ganesh Prasad Pokhariyal. On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. Am. J. Theor. Appl. Stat. 2018, 7(3), 92-101. doi: 10.11648/j.ajtas.20180703.11

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AMA Style

Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal. On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys. Am J Theor Appl Stat. 2018;7(3):92-101. doi: 10.11648/j.ajtas.20180703.11

Copy | Download

@article{10.11648/j.ajtas.20180703.11,
  author = {Conlet Biketi Kikechi and Richard Onyino Simwa and Ganesh Prasad Pokhariyal},
  title = {On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {3},
  pages = {92-101},
  doi = {10.11648/j.ajtas.20180703.11},
  url = {https://doi.org/10.11648/j.ajtas.20180703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180703.11},
  abstract = {In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys
AU  - Conlet Biketi Kikechi
AU  - Richard Onyino Simwa
AU  - Ganesh Prasad Pokhariyal
Y1  - 2018/03/24
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180703.11
DO  - 10.11648/j.ajtas.20180703.11
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  - 92
EP  - 101
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180703.11
AB  - In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. Generally the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.
VL  - 7
IS  - 3
ER  -

Copy | Download