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Approximation of Finite Population Totals Using Lagrange Polynomial
Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya
Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
- 1 Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya
- 2 Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
- 3 Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Open Journal of Statistics·Volume 07 (2017)·Pages 689–701·Published 21 July 2017·DOI10.4236/ojs.2017.74048
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Abstract
Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.
KeywordsLagrange PolynomialApproximationFinite Population TotalAuxiliary InformationLocal Polynomial RegressionHorvitz Thompson and Ratio Estimator
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