Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 3, June 2017, Pages: 122-128
Received: Apr. 17, 2017;
Accepted: May 27, 2017;
Published: Jun. 30, 2017
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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
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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).
Homoscedasticity, Jackknifing, Optimal, Robustness, Efficiency
To cite this article
Imboga Orang’o Herbert,
George Otieno Orwa,
Romanus Odhiambo Otieno,
Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing, International Journal of Theoretical and Applied Mathematics.
Vol. 3, No. 3,
2017, pp. 122-128.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
R. V. Allan Dorfman and R. Chambers. Estimation of Finite population distribution using non-parametric regression. Annals of statistics 21, 1452-21475, 1993.
R. V. Allan Dorfman and R. M Royall. Non-parametric regression for estimating population totals in finite populations. American Statistical Association, 1992.
Nadaraya, E. A. (1964) On Estimating Regression. Theory of Probability and Applications, 9, 141-142.
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.
Sanchez-Borrego, I. R. and Rueda, M. (2009) A Predictive Estimator of Finite Population Mean Using Nonparametric Regression. Computational Statistics, 24, 1-14.
Breidt, F. J. and Opsomer, J. D. (2000) Local Polynomial Regression Estimators in Survey Sampling.
Quenouille, M. H. (1949). Approximate tests of correlation in time series. J. R. Statist. Soc. B 11, 68-64.
Quenouille, M. H. (1956). Notes on bias in estimation. Biometrica 43, 54-60.
Otieno, R and Mwalili, T (2000) Non parametric regression for finite population estimation. East Africa Journal of Sience, Vol II, part 2, 107-112.