Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing

Imboga Orang’o Herbert; George Otieno Orwa; Romanus Odhiambo Otieno

doi:doi:10.11648/j.ijtam.20170303.14

| Peer-Reviewed

Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing

Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 3)

Received: 17 April 2017 Accepted: 27 May 2017 Published: 30 June 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ijtam.20170303.14
Page(s)	122-128
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), 2017. Published by Science Publishing Group

Keywords

Homoscedasticity, Jackknifing, Optimal, Robustness, Efficiency

References

[1]	C. Wu and R. Little. A model-Calibration approach to using complete auxiliary information from Survey data. Journal of American Statistical Association 96, 185-193, 2001.
[2]	R. V. Allan Dorfman and R. Chambers. Estimation of Finite population distribution using non-parametric regression. Annals of statistics 21, 1452-21475, 1993.
[3]	R. V. Allan Dorfman and R. M Royall. Non-parametric regression for estimating population totals in finite populations. American Statistical Association, 1992.
[4]	Nadaraya, E. A. (1964) On Estimating Regression. Theory of Probability and Applications, 9, 141-142.
[5]	Dorfman, A. H. (1992) Nonparametric Regression for Estimating Totals in Finite Population. In Section on Survey Research Methods. Journal of American Statistical Association, 622-625.
[6]	Sanchez-Borrego, I. R. and Rueda, M. (2009) A Predictive Estimator of Finite Population Mean Using Nonparametric Regression. Computational Statistics, 24, 1-14.
[7]	Breidt, F. J. and Opsomer, J. D. (2000) Local Polynomial Regression Estimators in Survey Sampling.
[8]	Quenouille, M. H. (1949). Approximate tests of correlation in time series. J. R. Statist. Soc. B 11, 68-64.
[9]	Quenouille, M. H. (1956). Notes on bias in estimation. Biometrica 43, 54-60.
[10]	Otieno, R and Mwalili, T (2000) Non parametric regression for finite population estimation. East Africa Journal of Sience, Vol II, part 2, 107-112.

Cite This Article

Plain Text BibTeX RIS

APA Style

Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno. (2017). Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. International Journal of Theoretical and Applied Mathematics, 3(3), 122-128. https://doi.org/10.11648/j.ijtam.20170303.14

Copy | Download

ACS Style

Imboga Orang’o Herbert; George Otieno Orwa; Romanus Odhiambo Otieno. Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. Int. J. Theor. Appl. Math. 2017, 3(3), 122-128. doi: 10.11648/j.ijtam.20170303.14

Copy | Download

AMA Style

Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno. Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. Int J Theor Appl Math. 2017;3(3):122-128. doi: 10.11648/j.ijtam.20170303.14

Copy | Download

@article{10.11648/j.ijtam.20170303.14,
  author = {Imboga Orang’o Herbert and George Otieno Orwa and Romanus Odhiambo Otieno},
  title = {Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {122-128},
  doi = {10.11648/j.ijtam.20170303.14},
  url = {https://doi.org/10.11648/j.ijtam.20170303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170303.14},
  abstract = {In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing
AU  - Imboga Orang’o Herbert
AU  - George Otieno Orwa
AU  - Romanus Odhiambo Otieno
Y1  - 2017/06/30
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170303.14
DO  - 10.11648/j.ijtam.20170303.14
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 122
EP  - 128
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170303.14
AB  - In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).
VL  - 3
IS  - 3
ER  -

Copy | Download

Author Information

Imboga Orang’o Herbert

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
Romanus Odhiambo Otieno

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno. (2017). Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. International Journal of Theoretical and Applied Mathematics, 3(3), 122-128. https://doi.org/10.11648/j.ijtam.20170303.14

Copy | Download

ACS Style

Imboga Orang’o Herbert; George Otieno Orwa; Romanus Odhiambo Otieno. Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. Int. J. Theor. Appl. Math. 2017, 3(3), 122-128. doi: 10.11648/j.ijtam.20170303.14

Copy | Download

AMA Style

Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno. Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. Int J Theor Appl Math. 2017;3(3):122-128. doi: 10.11648/j.ijtam.20170303.14

Copy | Download

@article{10.11648/j.ijtam.20170303.14,
  author = {Imboga Orang’o Herbert and George Otieno Orwa and Romanus Odhiambo Otieno},
  title = {Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {122-128},
  doi = {10.11648/j.ijtam.20170303.14},
  url = {https://doi.org/10.11648/j.ijtam.20170303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170303.14},
  abstract = {In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing
AU  - Imboga Orang’o Herbert
AU  - George Otieno Orwa
AU  - Romanus Odhiambo Otieno
Y1  - 2017/06/30
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170303.14
DO  - 10.11648/j.ijtam.20170303.14
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 122
EP  - 128
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170303.14
AB  - In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).
VL  - 3
IS  - 3
ER  -

Copy | Download