On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys
American Journal of Theoretical and Applied Statistics
Volume 7, Issue 3, May 2018, Pages: 92-101
Received: Feb. 10, 2018; Accepted: Mar. 6, 2018; Published: Mar. 24, 2018
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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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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.
Nonparametric Regression, Finite Population Totals, Local Linear Regression, Robustness Properties, Confidence Intervals, Model Based Surveys
To cite this article
Conlet Biketi Kikechi, Richard Onyino Simwa, Ganesh Prasad Pokhariyal, On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys, American Journal of Theoretical and Applied Statistics. Vol. 7, No. 3, 2018, pp. 92-101. doi: 10.11648/j.ajtas.20180703.11
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