INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 6, Issue 7, November 2017

Pages: 12-26

Date of Publication: 11-Nov-2017

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COMPARISON OF THE PIECEWISE POLYNOMIAL APPROXIMATE TO THE NEWTON BACKWARD DIFFERENCE POLYNOMIAL APPROXIMATE OF FINITE POPULATION TOTALS

Author: Lamin Kabareh1, Thomas Mageto2

Category: Engineering, Science and Mathematics

Abstract:

Approximation of finite population totals in the presence of auxiliary information is considered. Polynomials based on Piecewise polynomial and Newton backward difference polynomial are proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, these approximation techniques are based on annual population totals in order to fit in the best approximating polynomial within a given period of time (years) in this study. The proposed Piecewise polynomial technique has shown to be unbiased under a first order polynomial as we approach the target value as opposed to the Newton backward difference polynomial. The use of real data indicated that the Piecewise polynomial is efficient and can approximate properly and give a smooth curve at the knots in the presence of outliers.

Keywords: Piecewise polynomial, Newton backward difference polynomial, approximation, finite population total, auxiliary information, Local polynomial regression, Horvitz Thompson and Ratio estimator, outliers, knots.